Séminaire UQSay

2–3 PM — Claire Boyer (LMO, UPS)

A primer on physics-informed learning

Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a partial differential equation that quantifies the physical inconsistency. Practitioners often resort to physics-informed neural networks (PINNs) to solve this kind of problem. After discussing some strengths and limitations of PINNs, we prove that for linear differential priors, the problem can be formulated directly as a kernel regression task, giving a rigorous framework to analyze physics-informed ML. In particular, the physical prior can help in boosting the estimator convergence. We also propose the PIKL algorithm (PIKL for physics-informed kernel learning) as a numerical strategy to implement this kernel method.

References:

• Convergence and error analysis of PINNs, Bernoulli 2024
• Physics-informed machine learning as a kernel method, 2024
• Physics-informed kernel learning, 2024

Joint work with N. Doumèche (Sorbonne University) & G. Biau (Sorbonne University) & F. Bach (INRIA).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Sam Allen (ETH Zürich, Seminar of Statistics) — [slides]

Evaluating forecasts using positive definite kernels

Probabilistic forecasts take the form of probability distributions over the set of possible outcomes. To assess the quality of a probabilistic forecast, proper scoring rules condense forecast performance into a single numerical value, with which competing forecasters can be ranked and compared. Many popular scoring rules can be expressed in terms of positive definite kernels. This allows us to leverage well-established results on kernels when evaluating probabilistic forecasts. In this work, we discuss two useful connections between kernel methods and scoring rules. Firstly, we demonstrate that well-known weighted scoring rules correspond to kernel scores. Weighted scoring rules allow users to emphasise particular outcomes during forecast evaluation, and by expressing these as kernel scores, we introduce a broad generalisation of existing weighted scores that can be applied to probabilistic forecasts on arbitrary outcome domains. This facilitates the introduction of weighted multivariate scoring rules, for example. Secondly, we demonstrate that by embedding probabilistic forecasts into a Reproducing Kernel Hilbert Space (RKHS), estimating the parameters of forecast models by optimising a kernel score often corresponds to a convex quadratic optimisation problem, which can therefore be solved robustly and efficiently. This encompasses common forecast combination methods, such as linear pooling, providing a means to optimally combine competing forecasts made on arbitrary outcome domains. To illustrate the practical benefit of these results, the two applications of kernel scores are applied in case studies on operational weather forecasts..

References:

• Evaluating Forecasts for High-Impact Events Using Transformed Kernel Scores, 2023
• Weighted scoringRules: Emphasizing Particular Outcomes When Evaluating Probabilistic Forecasts, 2024 – [R package]- [Python package]

Joint work with D. Ginsbourger (University of Bern) & J. Ziegel (ETH Zürich).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Botond Szabo (Bocconi University, Department of Decision Sciences – BIDSA) — [slides]

Uncertainty quantification and estimation with variational Gaussian Processes

We study the theoretical properties of a variational Bayes method in the Gaussian Process regression model. We consider the inducing variables method introduced by Titsias (2009b) and derive sufficient conditions for obtaining contraction rates for the corresponding variational Bayes (VB) posterior. We also derive guarantees and limitations for the associated credible sets. The derived general results are then applied for several specific examples. Finally, we also consider approximation methods from probabilistic numerics (e.g. Lanczos iteration and conjugate gradient descent). We demonstrate their close relationship with the variational Bayes approach and provide guidelines for these approaches as well to obtain optimal (minimax) statistical inference.

References:

• Contraction rates for sparse variational approximations in Gaussian process regression, 2022
• Uncertainty quantification for sparse spectral variational approximations in Gaussian process regression, 2023
• Contraction rates for conjugate gradient and Lanczos approximate posteriors in Gaussian process regression, 2024

Joint work with H. van Zanten (Vrije Universiteit Amsterdam) & D. Nieman (Vrije Universiteit Amsterdam) & B. Stankewitz (University of Potsdam).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Nadège Polette (Mines Paris PSL – CEA DAM DIF) — [slides]

Mitigating Overconfidence in Bayesian Field Inversion thanks to Hyperparameters Sampling

The objective of Bayesian field inversion is to approximate the posterior distribution of a field thanks to indirect observations. Such problems have to face two issues, the infinite dimensionality of the field and the high number of forward model evaluations required to achieve MCMC convergence. In this study, the field to infer is assumed to be a particular realization of a random field and is modeled by its truncated Karhunen-Loève (KL) decomposition leading to a finite dimensional parametrization. The KL representation relies on an autocovariance function that depends on poorly known hyperparameters. The added value of our work is to introduce a new method, called change of measure, designed to deal with uncertain hyperparameters instead of deterministic ones. In practice, the hyperparameters are jointly sampled with the KL coordinates and the posterior distribution has a hierarchical Bayesian structure. In addition, to reduce the computational cost of the MCMC procedure, the likelihood is estimated with polynomial chaos surrogates of the forward model outputs. Applications on transient diffusion and seismic traveltime tomography problems highlight the interest of not fixing the hyperparameters to deterministic values. Exploring the hyperparameters space is highly valuable because it provides a better estimation of the field uncertainties.

References:

• Change of Measure for Bayesian Field Inversion with Hierarchical Hyperparameters Sampling, 2024

Joint work with O. Le Maître (CNRS, CMAP) & P. Sochala (CEA DAM DIF) & A. Gesret (Mines Paris PSL).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

4–5 PM — Habib Najm (Sandia National Laboratories) — [slides]

Uncertainty Quantification in Computational Combustion Models

Uncertainty quantification (UQ) in large scale computational combustion models faces key challenges of high dimensionality and computational cost. These models, particularly when using detailed chemical mechanisms, typically involve large numbers of uncertain parameters. Exploring these high-dimensional spaces necessitates the use of large numbers of computational samples, which, given high computational costs, is prohibitively expensive. I will discuss a UQ workflow, and underlying methods, to address this challenge in practice. These methods include global sensitivity analysis with polynomial chaos (PC) sparse regression, coupled with multilevel multifidelity methods. The combination of these tools is often useful to reliably cut-down dimensionality with acceptable computational costs, identifying a lower-dimensional subspace where the construction of PC surrogates of requisite accuracy is feasible. These surrogates are in turn necessary for both Bayesian inference and forward uncertainty propagation purposes. I will discuss this UQ workflow for problems of practical relevance in combustion. I will also touch on the issue of data availability, and the challenge of Bayesian estimation of uncertain model parameters given sparse or missing data.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Olivier Laurent (SATIE, Université Paris-Saclay – U2IS, ENSTA) — [slides]

A Symmetry-Aware Exploration of Bayesian Neural Network Posteriors

The distribution of modern deep neural networks (DNNs) weights — crucial for uncertainty quantification and robustness — is an eminently complex object due to its extremely high dimensionality. This paper presents one of the first large-scale explorations of the posterior distribution of deep Bayesian Neural Networks (BNNs), expanding its study to real-world vision tasks and architectures. Specifically, we investigate the optimal approach for approximating the posterior, analyze the connection between posterior quality and uncertainty quantification, delve into the impact of modes on the posterior, and explore methods for visualizing the posterior. Moreover, we uncover weight-space symmetries as a critical aspect for understanding the posterior. To this extent, we develop an in-depth assessment of the impact of both permutation and scaling symmetries that tend to obfuscate the Bayesian posterior. While the first type of transformation is known for duplicating modes, we explore the relationship between the latter and L2 regularization, challenging previous misconceptions. Finally, to help the community improve our understanding of the Bayesian posterior, we release a large-scale dataset of model checkpoints, including thousands of real-world models, along with our code.

References:

• A Symmetry-Aware Exploration of Bayesian Neural Network Posteriors, ICLR, 2024 – [webpage]- [code]
• TorchUncertainty package – [associated bdd]

Joint work with Emanuel Aldea (SATIE) & Gianni Franchi (U2IS, ENSTA).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

3–4 PM — Alexander Terenin (Cornell University) — [slides]

Sampling from Gaussian Process Posteriors using Stochastic Gradient Descent

The ability to deploy Gaussian-process-based decision-making systems such as Bayesian optimization at scale has traditionally been limited by computational costs arising from the need to solve large linear systems. The de facto standard for solving linear systems at scale is via the conjugate gradient algorithm – in particular, stochastic gradient descent is known to converge near-arbitrarily-slowly on quadratic objectives that correspond to Gaussian process models’ linear systems. In spite of this, we show that it produces solutions which have low test error, and quantify uncertainty in a manner that mirrors the true posterior. We develop a spectral characterization of the error caused by finite-time non-convergence, which we prove is small both near the data, and sufficiently far from the data. Stochastic gradient descent therefore only differs from the true posterior between these regions, demonstrating a form of implicit bias caused by benign non-convergence. We conclude by showing, empirically, that stochastic gradient descent achieves state-of-the-art performance on sufficiently large-scale regression tasks, and produces uncertainty estimates which match the performance of significantly more expensive baselines on large-scale Bayesian optimization.

References:

• Sampling from Gaussian Process Posteriors using Stochastic Gradient Descent, NeurIPS, 2023 – [github sgd-gp]
• Stochastic Gradient Descent for Gaussian Processes Done Right, ICLR, 2024
• Numerically Stable Sparse Gaussian Processes via Minimum Separation using Cover Trees, JMLR, 2024 – [github conjugate-gradient-sparse-gp]

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (L2S)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Gaël Poette (CEA DAM, CESTA – ENSEIRB-MATMECA) — [slides]

Building and solving reduced models for the uncertain linear Boltzmann equation (sometimes intrusiveness, a.k.a. physics-informedness, is worth it)

In this talk, I will present one way to build reduced models which aim at being able to efficiently propagate uncertainties through the linear Boltzmann equation. Only one run of a Monte-Carlo code will be enough to solve the system and accurately estimate statistical observables (mean, variance, tolerance intervals, sensitivity indices) on your physical observables of interest. From the Machine Learning community point of view, the presented reduced model can be cast in the category of ‘Physics Informed’ ones in the sense that the structure of the partial differential equation is intensively used in order to build the reduced model. In this context, we will show that such a physics-informed strategy (from the literature from another generation, it is also called an ‘intrusive’ strategy) combined with the relevant numerical scheme can be very competitive with respect to the best of the non-intrusive ones.

From the transport community point of view, the reduced model I will present can be understood, in a sense, as an attempt to make the best of two worlds: Pn reduced models and Monte-Carlo resolution schemes.The Pn model, well-known in neutronics and photonics, is built with respect to the uncertain variables (in the literature relative to uncertainty quantification, it is commonly called Polynomial Chaos) rather than with respect to the angular one. And the resulting reduced model is solved with a Monte-Carlo scheme (due to the high dimensional context we are in). The reasons for such a combination will be detailed and numerical results will be presented (for the instationary linear Boltzmann but also for eigenvalue computations). Performance comparisons will be presented on neutronics (keff computations) and photonics applications. If time allows it, discussions on the asymptotical errors (noise) will be tackled.

Some parts of this talk come from a joint work with Emeric Brun (CEA, DES).

References:

• G. Poëtte (2019) A gPC-intrusive Monte-Carlo scheme for the resolution of the uncertain linear Boltzmann equation. J. Comp. Phys. DOI:10.1016/j.jcp.2019.01.052,
• G. Poëtte (2020) Spectral convergence of the generalized Polynomial Chaos reduced model obtained from the uncertain linear Boltzmann equation. Mathematics and Computers in Simulation. 10.1016/j.matcom.2020.04.009.
• G. Poëtte (2021) Efficient uncertainty propagation for photonics: Combining implicit semi-analog monte carlo (ISMC) and monte carlo generalised polynomial chaos (MC-gPC). J. Comp. Phys. DOI:10.1016/j.jcp.2021.110807,
• G. Poëtte (2022) Numerical analysis of the Monte-Carlo noise for the resolution of the deterministic and uncertain linear Boltzmann equation (comparison of non-intrusive gPC and MC-gPC). J. of Comp. and Theor. Transport. DOI:10.1080/23324309.2022.2063900.
• G. Poëtte, E. Brun (2022) Efficient uncertain keff computations with the Monte Carlo resolution of generalised Polynomial Chaos based reduced models. J. Comp. Phys. DOI:10.1016/j.jcp.2022.111007.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).

Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

3–4 PM — John Jakeman (Sandia National Laboratories) — [slides]

Surrogate Modeling for Efficiently, Accurately and Conservatively Estimating Measures of Risk

This talk will present a surrogate-based framework for conservatively estimating risk from limited evaluations of an expensive physical experiment or simulation. Focus will be given to the computation of risk measures that quantify tail statistics of the loss, such as Average Value at Risk (AVaR). Monte Carlo (MC) sampling can be used to approximate such risk measures, however MC requires a large number of model simulations, which can make accurately estimating risk intractable for computationally expensive models. Given a set of samples surrogates are constructed such that the estimate of risk, obtained from the surrogate, is always greater than the empirical estimate obtained from the training data. These surrogates not only limit over-confidence in model reliability but produce estimates of risk that converge much faster to the true risk, than purely sampled based estimates.

The first part of the talk will discuss how to use the risk quadrangle, which rigorously connects stochastic optimization and statistical estimation, to construct conservative surrogates that can be tailored to the specific risk preferences of the model stakeholder. Surrogates constructed using least squares and quantile regression are specific cases of this framework. The second part of the talk will then present an approach, based upon stochastic orders, for constructing surrogates that are conservative with respect to families of risk measures, which is useful when risk preferences are difficult to elicit. This approach uses first and second order stochastic dominance to respectively enforce that the surrogate over-estimates probability of failure and AVaR for a finite set of thresholds. The conservative surrogates constructed introduce a bias that allows them to conservatively estimate risk. Theoretical results will be provided that show that for orthonormal models such as polynomial chaos expansions, this bias decays at the same rate as the root mean squared error in the surrogate. Numerous numerical examples will be used to confirm that that risk-aware surrogates do indeed overestimate risk while converging at the expected rate.

Reference: Surrogate modeling for efficiently, accurately and conservatively estimating measures of risk, RESS, 2022 – [github PyApprox].

Joint work with Drew Kouri (Sandia).

2–3 PM — Morgane Menz (IFPEN) — [slides]

Archissur: an Active Recovery of Constrained and Hidden Sets by SUR method. Coupling with adaptive space-filling and optimization

The analysis of simulated engineering systems (robust optimization, reliability assessment, …) generally requires numerous computationally expensive code simulations with different possible sets of values of design and environmental input variables. However, the simulators can encounter simulation crashes due to convergence issues for some values of both input variables. These failures correspond to a hidden constraint and might be as costly to evaluate as a feasible simulation. The presence of such crashes must be managed in a wise way, in order to target feasible input areas and thus avoid unnecessary irrelevant simulations.

In this context, we propose an adaptive strategy to learn the hidden constraint at a reduced numerical cost based only on a limited number of binary observations corresponding to failure or non-failure status. Our approach is a Gaussian Process Classifier active learning method based on Stepwise Uncertainty Reduction strategies to assess hidden constraints prediction. A numerically effective formulation of the enrichment criterion suited for classification is provided. Additionally, the proposed enrichment criterion is employed to address metamodeling and optimization in the presence of hidden constraints..

Reference: Estimation of simulation failure set with active learning based on Gaussian Process classifiers and random set theory, 2023.

Joint work with Miguel Munoz-Zuniga (IFPEN) & Delphine Sinoquet (IFPEN).

2–3 PM — Baptiste Kerleguer (CEA, DAM/DIF) — [slides]

A Bayesian neural network approach to multi-fidelity surrogate modeling

This talk deals with the surrogate modeling of computer code results that can be evaluated at different levels of accuracy and computational cost, called multi-fidelity. We propose a method combining Gaussian process (GP) regression on low-fidelity data and a Bayesian neural network (BNN) on high-fidelity data. The novelty, compared with the state of the art, is that uncertainties are taken into account at all fidelity levels. The prediction uncertainty of the low-fidelity level is transmitted by Gauss-Hermite quadrature to the high-fidelity level. In addition, this method takes into account non-nested designs of experiment and non-linear interactions between levels. The proposed approach is then compared to several multi-fidelity GP regression methods on analytic functions and on a computer code. Reference: A Bayesian neural network approach to multi-fidelity surrogate modeling, IJUQ 14.1, 2024. Joint work with Josselin Garnier (CMAP) & Claire Cannamela (CEA, DAM/DIF).

2–3 PM — Marouane Il Idrissi (EDF R&D – IMT) — [slides]

Generalized Hoeffding decomposition and the linear nature of non-linearity

Hoeffding’s decomposition of random outputs traditionally requires the inputs to be mutually independent. It allows uniquely decomposing a square-integrable function as a sum taken over every subset of inputs. Generalizing this result to non-mutually independent inputs has been a recent challenge in the literature on sensitivity analysis. Proposed solutions exist, but they require relatively restrictive assumptions on the distribution of the inputs. However, Hoeffding’s decomposition can be generalized under two reasonable assumptions on the inputs’ distribution: non-perfect functional dependence and non-degenerate stochastic dependence. This generalization requires approaching the problem using a framework at the cornerstone of probability theory, functional analysis, and combinatorics. From this perspective, it can be seen as finding a direct-sum decomposition of a particular Lebesgue space, unveiling a surprisingly linear approach to handling stochastic and functional non-linearities. The proposed « ortho-canonical decomposition » relies on oblique projections rather than the traditional conditional expectations. Ultimately, it allows the definition of intuitive and interpretable sensitivity indices, which offers a path toward a more precise uncertainty quantification. In this talk, we will delve into the unconventional framework used, discuss its nuances, and explore the various perspectives and challenges it offers. Reference: Understanding black-box models with dependent inputs through a generalization of Hoeffding’s decomposition, 2023 [github]. Joint work with Nicolas Bousquet (EDF R&D – LPSM), Fabrice Gamboa (IMT), Bertrand Ioss (EDF R&D – IMT) and Jean-Michel Loubes (IMT).

2–3 PM — Gabriel Sarazin (CEA Paris Saclay) — [slides]

Towards more interpretable kernel-based sensitivity analysis

When working with a computationally-expensive simulation code involving a large number of uncertain physical parameters, it is often advisable to perform a preliminary sensitivity analysis in order to identify which input variables will really be useful for surrogate modelling. On paper, the total-order Sobol’ indices fulfill this role perfectly, since they are able to detect any type of input-output dependence, while being interpretable as simple percentages of the output variance. However, in many situations, their accurate estimation remains a thorny issue, despite remarkable progress in that direction over the past few months. In this context where inference is strongly constrained, kernel methods have emerged as an excellent alternative, notably through the Hilbert-Schmidt independence criterion (HSIC). Although they offer undeniable advantages over Sobol’ indices, HSIC indices are much harder to understand, and this lack of interpretability is a major obstacle to their wider dissemination. In order to marry the advantages of Sobol’ and HSIC indices, an ANOVA-like decomposition allows to define HSIC-ANOVA indices at all orders, just as would be done for Sobol’ indices. This recent contribution is the starting point of this presentation. The main objective of this talk is to provide deeper insights into the HSIC-ANOVA framework. One major difference with the basic HSIC framework lies in the use of specific input kernels (like Sobolev kernels). First, a dive into the universe of cross-covariance operators will allow to better understand how sensitivity is measured by HSIC-ANOVA indices, and what type of input-output dependence is captured by each term of the HSIC-ANOVA decomposition. Then, a brief study of Sobolev kernels, focusing more particularly on their feature maps, will reveal what kind of simulators are likely to elicit HSIC-ANOVA interactions. It will also be demonstrated that Sobolev kernels are characteristic, which ensures that HSIC-ANOVA indices can be used to test input-output independence. Finally, a test procedure will be proposed for the total-order HSIC-ANOVA index, and it will be shown (numerically) that the resulting test of independence is at least as powerful as the standard test (based on two Gaussian kernels). Reference: New insights into the feature maps of Sobolev kernels: application in global sensitivity analysis, 2023 [sensiHSIC & testHSIC in R package sensitivity]. Joint work with Amandine Marrel (CEA Cadarache), Sébastien Da Veiga (ENSAI) and Vincent Chabridon (EDF R&D).

2–3 PM — Pierre Humbert (LMO – INRIA) — [slides]

One-Shot Federated Conformal Prediction

In this presentation, we will focus on a method for constructing prediction sets in a federated learning setting where only one round of communication between the agents and the server is allowed (one-shot). More precisely, by defining a particular estimator called the quantile-of-quantiles, we will prove that for any distribution, it is possible to produce marginally (and training-conditionally) valid prediction sets. Over a wide range of experiments, we will show that we are able to obtain prediction sets whose coverage and length are very similar to those obtained in a centralized setting, making our method particularly well-suited to perform conformal predictions in a one-shot federated learning setting. Reference: One-Shot Federated Conformal Prediction, ICML 2023 Joint work with Batiste Le Bars, Aurélien Bellet and Sylvain Arlot.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Michael I. Jordan (Berkeley, University of California.)

Prediction-Powered Inference

I introduce prediction-powered inference – a framework for performing valid statistical inference when an experimental data set is supplemented with predictions from a machine-learning system. Our framework yields provably valid conclusions without making any assumptions on the machine-learning algorithm that supplies the predictions. Higher accuracy of the predictions translates to smaller confidence intervals, permitting more powerful inference. Prediction-powered inference yields simple algorithms for computing valid confidence intervals for statistical objects such as means, quantiles, and linear and logistic regression coefficients. I demonstrate the benefits of prediction-powered inference with data sets from proteomics, genomics, electronic voting, remote sensing, census analysis, and ecology. Reference: A. Angelopoulos, S. Bates, C. Fannjiang, M. I. Jordan, T. Zrnic, “Prediction-Powered Inference”, 2023.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Christoph Molnar & Timo Freiesleben (Machine Learning in Science Cluster, University of Tübingen.) — [slides]

Supervised Machine Learning in Science

From folding proteins and predicting tornadoes to studying human nature — machine learning has changed science. Science always had an intimate relationship with prediction, but machine learning intensifies this focus. Can this hyper-focus on prediction models be justified? Can a machine learning model be part of a scientific model? Or are we on the wrong track? We explore and justify the use of supervised machine learning in science. However, a pure and naive application of supervised learning won’t get you far, because raw machine learning has so many insufficiencies that make it unusable in this form for science. Unintelligible models, lack of uncertainty quantification, lack of causality. But we already have all the puzzle pieces to fix machine learning, from incorporating domain knowledge and assuring the representativeness of the training data to robust, interpretable, and causal models. We bring together the philosophical justification and the solutions that make supervised machine learning a powerful tool for science.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Stefania Fresca (MOX, Dept. of Mathematics, Politecnico di Milano)

Deep learning-based reduced order models for the real-time approximation of parametrized PDEs

Conventional reduced order models (ROMs) anchored to the assumption of modal linear superimposition, such as proper orthogonal decomposition (POD), may reveal inefficient when dealing with nonlinear time-dependent parametrized PDEs, especially for problems featuring coherent structures propagating over time. To enhance ROM efficiency, we propose a nonlinear approach to set ROMs by exploiting deep learning (DL) algorithms, such as convolutional neural networks. In the resulting DL-ROM, both the nonlinear trial manifold and the nonlinear reduced dynamics are learned in a non-intrusive way by relying on DL algorithms trained on a set of full order model (FOM) snapshots, obtained for different parameter values. Performing then a former dimensionality reduction on FOM snapshots through POD enables, when dealing with large-scale FOMs, to speedup training times, and decrease the network complexity, substantially. Accuracy and efficiency of the DL-ROM technique are assessed on different parametrized PDE problems in cardiac electrophysiology, computational mechanics and fluid dynamics, possibly accounting for fluid-structure interaction (FSI) effects, where new queries to the DL-ROM can be computed in real-time. Moreover, numerical results obtained by the application of DL-ROMs to the solution of an industrial application, i.e. the approximation of the structural or the electromechanical behaviour of Micro-Electro-Mechanical Systems (MEMS), will be shown. References:

1. G. Gobat, S. Fresca, A. Manzoni, A. Frangi, “Reduced order modelling of nonlinear vibrating multiphysics microstructures with deep learning-based approaches”, Sensors, vol. 23, no. 6, pp. 3001, 2023 .
2. S. Fresca, G. Gobat, P. Fedeli, A. Frangi, A. Manzoni, “Deep learning-based reduced order models for the real-time simulation of the nonlinear dynamics of microstructures”, International Journal for Numerical Methods in Engineering, vol. 123, no. 20, pp. 4749-4777, 2022 .
3. S. Fresca, A. Manzoni, “POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition”, Computer Methods in Applied Mechanics and Engineering, vol. 388, pp. 114181, 2022 .
4. S. Fresca, A. Manzoni, L. Dede’, A. Quarteroni, “POD-enhanced deep learning-based reduced order models for the real-time simulation of cardiac electrophysiology in the left atrium”, Frontiers in Physiology, vol. 12, pp. 1431, 2021 .
5. S. Fresca, A. Manzoni, “Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models”, Fluids, vol. 6, no. 7, pp. 259, 2021 .
6. S. Fresca, A. Manzoni, L. Dede’, “A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs”, Journal of Scientific Computing, vol. 87, no. 2, pp. 1-36, 2021 .

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Sibo Cheng (Data Science Inst., Imperial College London) — [slides]

Machine learning and data assimilation for high dimensional dynamical systems

Data Assimilation (DA) and Machine Learning (ML) methods are extensively used in predicting and updating high-dimensional spatial-temporal dynamics. Typical applications span from computational fluid dynamics to geoscience and climate systems. In recent years, much effort has been given in combining DA and ML techniques with objectives including but not limited to dynamical system identification, reduced order surrogate modelling, error covariance specification and model error correction. This talk will provide an overview of state-of-the-art research in this interdisciplinary field, covering a wide range of applications. I will also present my unpublished work regarding efficient deep data assimilation with sparse observations and time-varying sensors. The proposed method, incorporating a deep learning inverse operator based on Voronoi tessellation into the assimilation objective function, is adept at handling sparse, unstructured, and time-varying sensor data. Reference: S. Cheng, C. Quilodran-Casas, S. Ouala, A. Farchi, C. Liu, P. Tandeo, R. Fablet, D. Lucor, B. Iooss, J. Brajard, D. Xiao, T. Janjic, W. Ding, Y. Guo, A. Carrassi, M. Bocquet and R. Arcucci, “Machine Learning With Data Assimilation and Uncertainty Quantification for Dynamical Systems: A Review”, IEEE/CAA Journal of Automatica Sinica, vol. 10, no. 6, pp. 1361–1387, June 2023.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Sophie Ricci (CECI, CERFACS & UMR 5318) — [slides]

On the merits of using remote sensing Earth Observation data to reduce uncertainties in flood forecasting with ensemble-based data assimilation

Flood simulation and forecast capability have been greatly improved thanks to advances in data assimilation (DA) strategies incorporating various types of observations; many are derived from spatial Earth Observation. This paper focuses on the assimilation of 2D flood observations derived from Synthetic Aperture Radar (SAR) images acquired during a flood event with a dual state-parameter Ensemble Kalman Filter (EnKF). Binary wet/dry maps are here expressed in terms of wet surface ratios (WSR) over a number of subdomains of the floodplain. This ratio is further assimilated jointly with in-situ water-level observations to improve the flow dynamics within the floodplain. However, the non-Gaussianity of the observation errors associated with SAR-derived measurements break a major hypothesis for the application of the EnKF, thus jeopardizing the optimality of the filter analysis. The novelty of this paper lies in the treatment of the non-Gaussianity of the SAR-derived WSR observations with a Gaussian anamorphosis process (GA). This DA strategy was validated and applied over the Garonne Marmandaise catchment (South-west of France) represented with the TELEMAC-2D hydrodynamic model, first in a twin experiment and then for a major flood event that occurred in January-February 2021. It was shown that assimilating SAR-derived WSR observations, in complement to the in-situ water-level observations significantly improves the representation of the flood dynamics. Also, the GA transformation brings further improvement to the DA analysis, while not being a critical component in the DA strategy. This study heralds a reliable solution for flood forecasting over poorly gauged catchments thanks to available remote-sensing datasets. Joint work with T. H. Nguyen & A. Piacentini (CECI, CERFACS), E. Simon (INP, IRIT), R. Rodriguez-Suquet & S. Peña-Luque (CNES).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Stefano Fortunati (LSS & IPSA) — [slides]

Matched, mismatched and semiparametric inference in elliptical distributions

Any scientific experiment, which aims to gain some knowledge about a real-word phenomenon, starts with the data collection. In statistics, all the available knowledge about a phenomenon of interest is summarized in the probability density function (pdf) of the collected observations. To this end, we define a model as the family of pdfs that are able to statistically characterize the observations. The most used classes of models are the parametric ones which however require the perfect match between the actual data distribution and the assumed model itself. Nevertheless, in practice, a certain amount of mismatch is often inevitable. Therefore, being aware about the possible performance loss that the derived estimator could undergone under model misspecification is of crucial importance. Even more important would be the possibility to overcome this misspecification problem. This can be achieved by adopting the more general semiparametric characterization of the statistical behavior of the collected data. In this seminar we use the set of elliptical distribution as “fil rouge” to analyse the three above-mentioned aspects. Joint work with F. Gini & M. S. Greco (University of Pisa, Italy), C. D. Richmond (Duke University, USA), A. M. Zoubir (TU Darmstadt, Germany), A. Renaux (L2S/UPS), F. Pascal (L2S/CentraleSupélec). References:

1. S. Fortunati, F. Gini, M. S. Greco and C. D. Richmond, “Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental Findings and Applications”, IEEE Signal Processing Magazine, vol. 34, no. 6, pp. 142-157, Nov. 2017.
2. S. Fortunati, F. Gini, M. S. Greco, A. M. Zoubir and and M. Rangaswamy, “Semiparametric Inference and Lower Bounds for Real Elliptically Symmetric Distributions”, IEEE Transactions on Signal Processing, vol. 67, no. 1, pp. 164-177, 1 Jan.1, 2019.
3. S. Fortunati, F. Gini, M. S. Greco, A. M. Zoubir and and M. Rangaswamy, “Semiparametric CRB and Slepian-Bangs Formulas for Complex Elliptically Symmetric Distributions”, IEEE Transactions on Signal Processing, vol. 67, no. 20, pp. 5352-5364, 15 Oct.15, 2019.
4. S. Fortunati, A. Renaux, F. Pascal, “Robust semiparametric efficient estimators in complex elliptically symmetric distributions”, IEEE Transactions on Signal Processing, vol. 68, pp. 5003-5015, 2020.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Felix Schneider (Technical University of Münich) — [slides]

Sparse Bayesian Learning for Rational Polynomial Chaos Expansion and Application in Structural Dynamics

Surrogate models enable efficient propagation of uncertainties in computationally demanding models of physical systems. We employ surrogate models that draw upon polynomial bases to model the stochastic frequency response of structural dynamics systems subject to parameter uncertainty. Therein, we define a rational polynomial chaos expansion (rPCE) as the ratio of two polynomial chaos expansions. The rPCE is thereby specifically suitable for models that include poles in the system response. We apply least squares and Bayesian regression techniques to determine the numerator and denominator coefficients, which allows straightforward coupling of the proposed methods with existing black-box solvers. This webinar focusses on a sparse Bayesian learning approach for the determination of the surrogate model coefficients in the rPCE. Due to the non-linearity of the surrogate with respsect to the denominator coefficients, we resort to a sequential solution strategy that utilizes the availability of a closed-form solution for the posterior distribution of the numerator coefficients. Subsequently, Laplace’s approximation is used to approximate the posterior distribution of the denominator coefficients. The coefficients and an optimal set of hyperparameters are then found in a sequential manner. We compare the performance with previously proposed strategies, which do not consider the uncertainty related to the denominator coefficients. Joint work with Iason Papaioannou & Gerhard Müller References:

1. F. Schneider, I. Papaioannou, M. Ehre and D. Straub. Polynomial chaos based rational approximation in linear structural dynamics with parameter uncertainties. Computers & Structures 233, 2020.
2. F. Schneider, I. Papaioannou, G. Müller, Sparse Bayesian Learning for Complex‐Valued Rational Approximations. International Journal for Numerical Methods in Engineering, 2022.
3. F. Schneider, I. Papaioannou, D. Straub, C. Winter, G. Müller, Bayesian parameter updating in linear structural dynamics with frequency transformed data using rational surrogate models. Mechanical Systems and Signal Processing 166, 2022.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Yingfan Wang (Interpretable ML Lab, Duke Univ.) — [slides]

Understanding principles for dimensionality reduction tools, and PaCMAP for data visualization

Dimension reduction (DR) techniques such as t-SNE, UMAP, and TriMap have demonstrated impressive visualization performance on many real-world datasets. One tension that has always faced these methods is the trade-off between preservation of global structure and preservation of local structure. In this work, our main goal is to understand what aspects of DR methods are important for preserving both local and global structure. Towards the goal of local structure preservation, we provide several useful design principles for DR loss functions based on our new understanding of the mechanisms behind successful DR methods. Towards the goal of global structure preservation, our analysis illuminates that the choice of which components to preserve is important. We leverage these insights to design a new algorithm for DR, called Pairwise Controlled Manifold Approximation Projection (PaCMAP), which preserves both local and global structure. Joint work with H. Huang, C. Rudin & Y. Shaposhnik. References:

1. Wang, Y., Huang, H., Rudin, C. & Shaposhnik, Y. (2021). Understanding how dimension reduction tools work: an empirical approach to deciphering t-SNE, UMAP, TriMAP, and PaCMAP for data visualization. Journal of Machine Learning Research 22.1, 9129-9201. DOI:10.5555/3546258.3546459,
2. Huang, H., Wang, Y., Rudin, C. & Browne, E.P. (2022). Towards a comprehensive evaluation of dimension reduction methods for transcriptomic data visualization. Communications biology 5, 719. DOI:10.1038/s42003-022-03628-x.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

3–4 PM — Andrew Gordon Wilson (New York University)

Myths and Legends of Bayesian Deep Learning

Bayesian inference makes more sense for modern neural networks than virtually every other model class, because these models can represent many compelling and complementary explanations for data, corresponding to different settings of their parameters. However, a number of myths have emerged about modern Bayesian deep learning. In this talk we will evaluate the following questions: (1) is Bayesian deep learning practical? (2) are standard (e.g. Gaussian) priors arbitrary and poor? (3) is « deep ensembles » a non-Bayesian competitor to standard approximate inference approaches? (4) does the common practice of posterior tempering, leading to « cold posteriors », mean the Bayesian posterior is poor? (5) is the marginal likelihood a reasonable way to select between trained networks? I will also discuss the success stories, future opportunities, and challenges in Bayesian deep learning. References:

1. Bayesian Deep Learning and a Probabilistic Perspective of Generalization (arXiv:2002.08791)
2. What are Bayesian Neural Network Posteriors Really Like? (arXiv:2104.14421)
3. Dangers of Bayesian Model Averaging under Covariate Shift (arXiv:2106.11905)
4. On Uncertainty, Tempering, and Data Augmentation in Bayesian Classification (arXiv:2203.16481)
5. Bayesian Model Selection, the Marginal Likelihood, and Generalization (arXiv:2202.11678)
6. Residual Pathway Priors for Soft Equivariance Constraints (arXiv:2112.01388)

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Paul Novello (DEEL – IRT Saint-Exupery – ANITI ) — [slides]

Making Sense of Dependence: Efficient Black-box Explanations Using Dependence Measure

In this talk, we present a new efficient black-box attribution method based on Hilbert-Schmidt Independence Criterion (HSIC), a dependence measure based on Reproducing Kernel Hilbert Spaces (RKHS). HSIC measures the dependence between regions of an input image and the output of a model based on kernel embeddings of distributions. It thus provides explanations enriched by RKHS representation capabilities. HSIC can be estimated very efficiently, significantly reducing the computational cost compared to other black-box attribution methods. Our experiments show that HSIC is up to 8 times faster than the previous best black-box attribution methods while being as faithful. Indeed, we improve or match the state-of-the-art of both black-box and white-box attribution methods for several fidelity metrics on Imagenet with various recent model architectures. Importantly, we show that these advances can be transposed to efficiently and faithfully explain object detection models such as YOLOv4. Finally, we extend the traditional attribution methods by proposing a new kernel enabling an ANOVA-like orthogonal decomposition of importance scores based on HSIC, allowing us to evaluate not only the importance of each image patch but also the importance of their pairwise interactions. Joint work with T. Fel & D. Vigouroux. References: arXiv.2206.06219 & github.com/paulnovello.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Oindrila Kanjilal (T.U. Munich) — [slides]

Reliability assessment of structural dynamic systems by importance sampling

Engineering structures are sometimes exposed to disastrous dynamic loading, such as strong wind and seismic motions. Structural failure due to these loads leads to significant economic loss and societal distress. Prediction of reliability during the service time is therefore essential in the design of new or integrity assessment of existing structures. Developments in computational mechanics provide tools to predict structural performance by means of simulation models. However, the parameters of these models, such as loading, material and geometric properties, deterioration processes and boundary conditions, can be seldom determined uniquely as they are affected by uncertainty and randomness. Model-based dynamic reliability assessment involves propagation of the input uncertainties through the model and exploration of the tails of the system response. This webinar focuses on Monte Carlo simulation (MCS)-based computational approaches to estimate the reliability. The main challenge in applying MCS lies in controlling the sampling variance of the failure probability estimator; the aim is to obtain probability estimates of acceptable accuracy with a small number of computational model runs. In this talk we will discuss recently developed advanced Monte Carlo techniques based on important sampling to address this challenge. Joint work with I. Papaioannou & D. Straub. References:

• Kanjilal, O., Papaioannou, I., & Straub, D. (2021). Cross entropy-based importance sampling for first-passage probability estimation of randomly excited linear structures with parameter uncertainty. Structural Safety 91, 102090. DOI:10.1016/j.strusafe.2021.102090,
• Kanjilal, O., Papaioannou, I., & Straub, D. (2022). Series system reliability of uncertain linear structures under Gaussian excitation by cross entropy-based importance sampling. ASCE Journal of Engineering Mechanics 148 (1), 04021136. 10.1061/(ASCE)EM.1943-7889.0002015.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Brian Staber (Safran Tech) — [slides]

Quantitative performance evaluation of Bayesian neural networks

Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Various approaches have been investigated including Bayesian neural networks, ensembles, deterministic approximations, amongst others. Despite the growing litterature about uncertainty quantification in deep learning, the quality of the uncertainty estimates remains an open question. In this work, we attempt to assess the performance of several algorithms on sampling and regression tasks by evaluating the quality of the confidence regions and how well the generated samples are representative of the unknown target distribution. Towards this end, several sampling and regression tasks are considered, and the selected algorithms are compared in terms of coverage probabilities, kernelized Stein discrepancies, and maximum mean discrepancies. Joint work with Sébastien Da Veiga (ENSAI). Ref: arXiv:2206.06779

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Felipe Tobar (Initiative for Data & AI, Universidad de Chile) — [slides]

Computationally-efficient initialisation of Gaussian processes: The generalised variogram method

We present a computationally-efficient strategy to find the hyperparameters of a Gaussian process (GP) avoiding the computation of the likelihood function. Motivated by the fact that training a GP via ML is equivalent (on average) to minimising the KL-divergence between the true and learnt model, we set to explore different metrics/divergences among GPs that are computationally inexpensive and provide estimates close to those of ML. In particular, we identify the GP hyperparameters by projecting the empirical covariance or (Fourier) power spectrum onto a parametric family, thus proposing and studying various measures of discrepancy operating on the temporal or frequency domains. Our contribution extends the Variogram method developed by the geostatistics literature and, accordingly, it is referred to as the Generalised Variogram method (GVM). In this talk, we will start with a brief introduction to Gaussian processes, then present the proposed GVM and finally provide experimental validation using synthetic and real-world data. Joint work with Elsa Cazelles & Taco de Wolff. Ref: arXiv:2210.05394.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Georgios Karagiannis (Durham University)

Bayesian spanning treed co-kriging for high dimensional output emulation

We propose a new Bayesian emulator, called Bayesian spanning treed co-kriging, suitable to analyze computer models with non-stationary massive outputs in the multifidelity setting. Our motivation comes from a real-life application with a storm surge simulator. Given certain assumptions on the Bayesian model, we introduce a suitable stochastic mechanism that facilitates predictions in a principal manner. The good performance of our method is demonstrated in benchmark examples, while our method is implemented for the analysis of a surge simulator given simulations at different fidelity levels.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Cécile Mercadier (Institut Camille Jordan) — [slides]

Hoeffding–Sobol and Möbius decompositions for (tail-)dependence analysis

Methods to analyse dependence and tail dependence are well established. Using for instance the copula function or the stable tail dependence function, and their empirical versions, one can construct non parametric statistics, parametric inference, as well as testing or resampling procedures. My talk will reflect upon the use of g sensitivity analysis for extreme value theory and copula modeling. Through my recent publications, I will explain what their links are and the benefit in mixing these domains. Joint work with Christian Genest, Paul Ressel & Olivier Roustant. Refs:

• C. Mercadier, O. Roustant & C. Genest (2022). Linking the Hoeffding–Sobol and Möbius formulas through a decomposition of Kuo, Sloan, Wasilkowski, and Wozniakowski. Statistics & Probability Letters, vol. 185 [hal-03220809],
• C. Mercadier & P. Ressel (2021). Hoeffding–Sobol decomposition of homogeneous co-survival functions: from Choquet representation to extreme value theory application. Dependence Modeling, 9(1):179–198 [hal-03200817],
• C. Mercadier & O. Roustant (2019). The tail dependograph. Extremes, 22:343–372 [hal-01649596].

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Gilles Stoltz (LMO, Université Paris-Saclay – CNRS) — [slides]

Multi-armed bandit problems: a statistical view, focused on lower bounds

Multi-armed bandit problems correspond to facing K unknown probability distributions, having to sequentially pull one of them, and observing a realization thereof at each pull. Two goals will be considered. (1) The realizations are payoffs, and the sum of these payoffs is to be maximized. This goal is achieving by minimizing regret, which is defined as the expected performance of the best arm minus the expected sum of payoffs achieved by a strategy. Two types of bounds may be defined, depending on whether they may depend on the specific bandit problem or only on the model (the class of possible distributions). We will recall classical strategies like UCB and MOSS, as well as a new strategy combining both, called KL-UCB-Switch. We will review upper bounds on the regret and detail which lower bounds may be achieved, and how. We will deal with one interesting extension, the adaptation to the unknown range of the distributions, i.e., when the distribution are supported on a compact interval that is unknown as well. The case of regret minimization is very well understood in the literature, contrary to: (2) A second goal can be to identify the best arm, i.e., control the probability that after T observations (sampled adaptively) the strategy does not identify the arm with the highest expectation. This is called best arm identification with a fixed budget. Limited results are available. We will describe a typical strategy, called successive rejects, that drops one distribution after the other after horse racing them. We will also indicate how we are currently laying the foundations of a non-parametric approach to this problem, based on KL divergences, as opposed to typical approaches based on differences between expectations. Joint work with Antoine Barrier, Aurélien Garivier, Hédi Hadiji & Pierre Ménard. Refs:

• KL-UCB-Switch: JMLR, 23(179):1−66, 2022,
• Lower bounds for regret minimization: MOOR, 4(2):377-766, 2019 [HAL],
• Adaptation to the unknown range: HAL-02794382,
• Best-arm identification: HAL-03792668.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Jonas Latz (Heriot-Watt University, Edinburgh) — [slides]

Stochastic gradient descent in continuous time: discrete and continuous data

Optimisation problems with discrete and continuous data appear in statistical estimation, machine learning, functional data science, robust optimal control, and variational inference. The « full » target function in such an optimisation problem is given by the integral over a family of parameterised target functions with respect to a discrete or continuous probability measure. Such problems can often be solved by stochastic optimisation methods: performing optimisation steps with respect to the parameterised target function with randomly switched parameter values. In this talk, we discuss a continuous-time variant of the stochastic gradient descent algorithm. This so-called stochastic gradient process couples a gradient flow minimising a parameterised target function and a continuous-time ‘index’ process which determines the parameter. We first briefly introduce the stochastic gradient processes for finite, discrete data which uses pure jump index processes. Then, we move on to continuous data. Here, we allow for very general index processes: reflected diffusions, pure jump processes, as well as other Lévy processes on compact spaces. Thus, we study multiple sampling patterns for the continuous data space. We show that the stochastic gradient process can approximate the gradient flow minimising the full target function at any accuracy. Moreover, we give convexity assumptions under which the stochastic gradient process with constant learning rate is geometrically ergodic. In the same setting, we also obtain ergodicity and convergence to the minimiser of the full target function when the learning rate decreases over time sufficiently slowly. Joint work with Kexin Jin, Chenguang Liu & Carola-Bibiane Schönlieb. Refs: DOI:10.1007/s11222-021-10016-8, arXiv:2112.03754, arXiv:2203.11555.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Mélanie Rochoux (CECI, Cerfacs, CNRS) — [slides]

Assimilating fire front position and emulating boundary-layer flow simulations for wildland fire behavior ensemble prediction and reanalysis

Monitoring wildfire behavior has recently emerged as a key public policy issue due to the occurrence of extreme events, in particular in the Euro-Mediterranean area that is exposed to more frequent and more severe wildfires under climate change. Key to this modeling is the development of an event-scale numerical simulation capability as a means to understand and predict the interactions between the atmosphere and the wildfire that drive its behavior. In this framework, my research aims at designing and evaluating a wildland fire behavior reanalysis capability to reconstruct as best as possible wildland fire progression at landscape-to-atmospheric scales. This approach combines information coming from a coupled atmosphere/fire model (Costes et al. 2021) and from airborne thermal infrared images (Paugam et al. 2021) through an ensemble-based data assimilation algorithm that infers more realistic environmental factors and estimates the time-evolving fire front position. My talk will provide an overview of the different components required to build this reanalysis capability, with two main focus: i) a front data assimilation methodology to address position errors in the fire front progression (Rochoux et al. 2018; Zhang et al. 2019), and ii) a non-intrusive reduced-order modeling approach combining principal component analysis and adaptive Gaussian processes to accurately and efficiently explore the physical parameter space and predict the atmospheric boundary-layer flow patterns (Nony et al. 2021). In the long-term, these methods will be applied to the Meso-NH/Blaze coupled atmosphere/fire model to design a wildland fire behavior ensemble prediction and reanalysis capability. Joint work with Bastien Nony & Thomas Jaravel (Cerfacs), Didier Lucor (LISN), Annabelle Collin & Philippe Moireau (Inria), Cong Zhang & Arnaud Trouvé (University of Maryland). Refs:

• M.C. Rochoux, A. Collin, C. Zhang, A. Trouvé, D. Lucor and P. Moireau (2018). Front shape similarity measure for shape-oriented sensitivity analysis and data assimilation for eikonal equation. ESAIM: Proceedings and Surveys, EDP Sciences, 63:258–279, DOI:10.1051/proc/201863258.
• C. Zhang, A. Collin, P. Moireau, A. Trouvé and M.C. Rochoux (2019). State-parameter estimation approach for data-driven wildland fire spread modeling: application to the 2012 RxCADRE S5 field-scale experiment. Fire Safety Journal, 105:286–299, DOI:<10.1016/j.firesaf.2019.03.009.
• B.X. Nony, M.C. Rochoux, D. Lucor and T. Jaravel (2021). Compound parametric metamodeling of large-eddy simulations for micro-scale atmospheric dispersion. 20th International Conference on Harmonisation within Atmospheric Dispersion Modelling for Regulatory Purposes, Tartu (Estonia), 14–18 June, 2021.
• A. Costes, M.C. Rochoux, C. Lac and V. Masson (2021) Subgrid-scale fire front reconstruction for ensemble coupled atmosphere-fire simulations of the FireFlux I experiment. Fire Safety Journal, 126:103475, DOI:10.1016/j.firesaf.2021.103475.
• R. Paugam, M.J. Wooster, W.E. Mell, M.C. Rochoux, J-B. Filippi, G. Rücker, O. Frauenberger, E. Lorenz, W. Schroeder and N. Govendor (2021). Orthorectification of helicopter-borne high resolution experimental burn observation from infra red handheld imagers. Remote Sensing, 13(23):4913, DOI:10.3390/rs13234913.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Nathalie Bartoli (ONERA) — [slides]

Bayesian optimization to solve mono- or multi-fidelity constrained black box problem

This work aims at developing new methodologies to optimize computational ostly complex systems (e.g., aeronautical engineering systems). The proposed surrogate-based method (often called Bayesian Optimization) uses adaptive sampling to promote a trade-off between exploration and exploitation. Our in-house implementation, called SEGOMOE, handles a high number of design variables (continuous, discrete or categorical) and nonlinearities by combining mixtures of experts (local surrogate models) for the objective and/or the constraints. An extension to multi-fidelity is also included when a variety of information is available. The performance of the proposed approach has been evaluated on both a benchmark of analytical constrained and unconstrained problems a well as a set of realistic aeronautical applications. Refs:

1. P. Saves, N. Bartoli, Y. Diouane, T. Lefebvre, J. Morlier, C. David, S. Defoort (2022). Multidisciplinary design optimization with mixed categorical variables for aircraft design. In AIAA SCITECH 2022 Forum (p. 0082).
2. R. C. Arenzana, A. López-Lopera, S. Mouton, N. Bartoli, T. Lefebvre (2021, July). Multifidelity Gaussian Process model for CFD and Wind Tunnel data fusion. In Proceedings of the International Conference on Multidisciplinary Design Optimization of Aerospace Systems (AEROBEST 2021) (pp. 1-758).
3. R. Priem, H. Gagnon, I. Chittick, S. Dufresne, Y. Diouane, and N. Bartoli (2020). An efficient application of Bayesian optimization to an industrial MDO framework for aircraft design. In AIAA AVIATION 2020 FORUM (p. 3152).
4. R. Priem, N. Bartoli, Y. Diouane, A. Sgueglia (2020), Upper trust bound feasibility criterion for mixed constrained Bayesian optimization with application to aircraft design, Aerospace Science and Technology
5. M. Meliani, N. Bartoli, T. Lefebvre, M.-A. Bouhlel, J. R. R. A. Martins, J. Morlier, Multi-fidelity efficient global optimization: Methodology and application to airfoil shape design, 20th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, June 2019, Dallas, United States
6. N. Bartoli, T. Lefebvre, S. Dubreuil, R. Olivanti, R. Priem, N. Bons, J. R. R. A. Martins, J. Morlier (2019), Adaptive modeling strategy for constrained global optimization with application to aerodynamic wing design, Aerospace Science and Technology Journal, vol. 90, p. 85-102
7. M.-A. Bouhlel, J. T. Hwang, N. Bartoli, R. Lafage, J. Morlier, J. R. R. A. Martins (2019), A Python surrogate modeling framework with derivatives, Advances in Engineering Software
8. M.-A. Bouhlel, N. Bartoli, A. Otsmane and J. Morlier, Improving kriging surrogates of high-dimensional design models by Partial Least Squares dimension reduction, Structural and Multidisciplinary Optimization, vol 53, no5, pp 935-952, 2016

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Nicola Pedroni (Politecnico di Torino) — [slides]

Quantification of Mixed Aleatory and Epistemic Uncertainties for Robust Design Optimization, in the Presence of Scarce and Functional Data

The quantitative analyses of the phenomena occurring in complex, safety-critical (e.g., civil, nuclear, aerospace and chemical) dynamic engineering systems are based on mathematical models. In practice, not all the characteristics of the system under analysis can be captured in the model: thus, uncertainty is present in the values of the input parameters and in the model hypotheses and structure. This is due to: (i) the intrinsically random nature of several of the phenomena occurring during system operation (aleatory uncertainty, here represented by multivariate probability distributions); (ii) the incomplete knowledge about some phenomena and operating conditions, often due to the scarcity of quantitative data available, which may be either very sparse or prohibitively expensive to collect (epistemic uncertainty, here described by intervals or sets). The characterization and quantification of this mixed uncertainty is of paramount importance for: (i) making robust decisions in safety-critical systems applications; (ii) optimally designing and operating such systems; and (iii) driving resource allocation for uncertainty reduction. This talk addresses the “NASA Langley Uncertainty Quantification Challenge on Optimization Under Uncertainty” with respect to two issues: (i) calibration of the mathematical model of an aerospace system and joint quantification of mixed (probabilistic) aleatory and (set-based) epistemic uncertainties; and (ii) system design optimization, in the presence of scarce and functional (time series) data (i.e., observations coming from the real system). With reference to issue (i), the parametric Sliced Normal (SN) class of distributions is employed, whose flexibility and versatility allow characterizing multivariate data and complex parameter dependencies with minimal effort. The modeling power of SNs is tested within a frequentist (optimization-based) framework and a Bayesian inverse approach. With reference to issue (ii), an iterative framework is developed to robustly optimize the design of the system (e.g., by minimizing the worst-case, epistemic upper bound of its failure probability). The issue is addressed by an efficient combination of: (i) Monte Carlo Simulation (MCS) to propagate the aleatory uncertainty described by probability distributions; (ii) Genetic Algorithms (GAs) to solve the optimization problems related to the propagation of epistemic uncertainty by interval analysis; and (iii) fast-running Artificial Neural Networks (ANNs) to reduce the computational time related to the repeated model evaluations. As a final remark, since the outputs of the system models of interest are functions of time, both issues are addressed in the space defined by the orthonormal bases resulting from a Singular Value Decomposition (SVD) of the real system observations. Ref: DOI:10.1016/j.ymssp.2021.108206.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — D. Austin Cole (GlaxoSmithKline, Inc.) — [slides]

Locally induced Gaussian processes for modelling large-scale simulations

Gaussian processes (GPs) serve as flexible surrogates for complex surfaces, but buckle under the cubic cost of matrix decompositions with big training data sizes. Geospatial and machine learning communities suggest pseudo-inputs, or inducing points, as one strategy to obtain an approximation easing that computational burden. However, we show how placement of inducing points and their multitude can be thwarted by pathologies, especially in large-scale dynamic response surface modeling tasks. As a remedy, we suggest porting the inducing point idea, which is usually applied globally, over to a more local context where selection is both easier and faster. In this way, our proposed methodology (LIGP) hybridizes global inducing point and data subset-based local GP approximation. A cascade of strategies for planning the selection of local inducing points is provided, and comparisons are drawn to related methodology with emphasis on computer surrogate modeling applications. We show that local inducing points extend their global and data-subset component parts on the accuracy—computational efficiency frontier. Next, we show how LIGP also provides benefits for stochastic simulation experiments by separating signal from noise with nugget estimation and replication. Woodbury identities allow local kernel structure to be expressed in terms of unique design locations only, increasing the amount of data (i.e., the neighborhood size) that may be leveraged without additional flops. Illustrative examples are provided on benchmark data and a variety of real-world simulation experiments, including satellite drag and epidemic management. Joint work with Ryan Christianson, Robert B. Gramacy and Mike Ludkovski. Ref: DOI:10.1007/s11222-021-10007-9 and arXiv:2109.05324.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Nora Lüthen (ETH Zürich) — [slides]

Poincaré chaos expansions for derivative-enhanced surrogate modelling and sensitivity analysis

Variance-based global sensitivity analysis, and in particular Sobol’ analysis, is widely adopted to determine the importance of input variables to a computational model. Sobol’ indices can be computed cheaply based on spectral methods like polynomial chaos expansions (PCE). Another option is given by the recently developed Poincaré chaos expansions (PoinCE), whose orthonormal tensor-product basis is generated from the eigenfunctions of one-dimensional Poincaré differential operators. The Poincaré differential operator is a special case of Sturm-Liouville operator and has recently been revisited for sensitivity analysis (Roustant et al. 2017). Solving the associated eigenproblem yields the Poincaré constant for a large class of one-dimensional measures with bounded support. The associated eigenfunctions form an orthonormal basis with the special (and characterizing) property that derivatives of the basis form again an orthogonal basis with respect to the same measure (Lüthen et al. 2021). The expansion of a model in terms of this basis allows the analytical computation of Sobol’ indices and derivative-based sensitivity indices (DGSM) directly from the expansion coefficients. Furthermore, the special property of the derivatives makes PoinCE particularly well suited to account for derivative information in the computation of sensitivity indices (Roustant et al. 2020). Indeed the expansions involving either model or derivative evaluations are connected, and computations can be reused. Assuming that partial derivative evaluations of the computational model are available, we compute spectral expansions in terms of Poincaré basis functions or basis partial derivatives, respectively, by sparse regression. We show on numerical examples that the derivative-based expansions provide accurate estimates for Sobol’ indices, even outperforming PCE in terms of bias and variance, and explore the performance of PoinCE as a surrogate model. Joint work with Olivier Roustant, Fabrice Gamboa, Bertrand Iooss, Stefano Marelli and Bruno Sudret. Ref: arXiv:2107.00394.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Didier Dubois (CNRS, IRIT, Univ. Paul Sabatier)

New uncertainty theories (The limited expressiveness of single probability measures) — [slides]

The variability of physical phenomena and partial ignorance about them motivated the development of probability theory in the two last centuries. However, the mathematical framework of probability theory, together with the Bayesian credo claiming the inevitability of unique probability measures for representing agents’ beliefs, have blurred the distinction between variability and ignorance. Modern theories of uncertainty, by putting together probabilistic and set-valued representations of information, provide a better account of the various facets of uncertainty.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (DOTA), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Gianni Franchi (U2IS, ENSTA Paris) — [slides]

Encoding the latent posterior of Bayesian neural networks for Uncertainty Quantification

Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior distribution of the network parameters, most BNN approaches are either limited to small networks or rely on constraining assumptions such as parameter independence. These drawbacks have enabled prominence of simple, but computationally heavy approaches such as Deep Ensembles, whose training and testing costs increase linearly with the number of networks. In this work we aim for efficient deep BNNs amenable to complex computer vision architectures, e.g. ResNet50 DeepLabV3+, and tasks, e.g. semantic segmentation, with fewer assumptions on the parameters. We achieve this by leveraging variational autoencoders (VAEs) to learn the interaction and the latent distribution of the parameters at each network layer. Our approach, Latent-Posterior BNN (LP-BNN), is compatible with the recent BatchEnsemble method, leading to highly efficient ({in terms of computation and} memory during both training and testing) ensembles. LP-BNNs attain competitive results across multiple metrics in several challenging benchmarks for image classification, semantic segmentation and out-of-distribution detection. Joint work with Andrei Bursuc, Emanuel Aldea, Séverine Dubuisson & Isabelle Bloch Ref: arXiv:2012.02818

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Didier Clouteau (MSSMAT), Amélie Fau (LMT), Filippo Gatti (MSSMAT), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (DOTA), Fernando Lopez-Caballero (MSSMAT), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Luc Pronzato (CNRS, Univ. Côte d’Azur) — [slides]

Maximum Mean Discrepancy, Bayesian integration and kernel herding for space-filling design

A standard objective in computer experiments is to predict/interpolate the behaviour of an unknown function f on a compact domain from a few evaluations inside the domain. When little is known about the function, space-filling design is advisable: typically, points of evaluation spread out across the available space are obtained by minimizing a geometrical (for instance, minimax-distance) or a discrepancy criterion measuring distance to uniformity. We focus our attention to sequential constructions where design points are added one at a time. The presentation is based on the survey [4], built on several recent results [2, 5, 6] that show how energy functionals can be used to measure distance to uniformity. We investigate connections between design for integration of f with respect to a measure µ (quadrature design), construction of the (continuous) BLUE for the location model, and minimization of energy (kernel discrepancy) for signed measures. Integrally strictly positive definite kernels define strictly convex energy functionals, with an equivalence between the notions of potential and directional derivative showing the strong relation between discrepancy minimization and more traditional design of optimal experiments, as used for instance in [3]. Kernel herding algorithms, which are special instances of vertex-direction methods used in optimal design [1, 7], can be applied to the construction of point sequences with suitable space-filling properties. Several illustrative examples are presented Refs:

1. F. Bach, S. Lacoste-Julien, and G. Obozinski. On the equivalence between herding and conditional gradient algorithms. In Proc. 29th Annual International Conference on Machine Learning, pages 1355–1362, 2012.
2. S.B. Damelin, F.J. Hickernell, D.L. Ragozin, and X. Zeng. On energy, discrepancy and group invariant measures on measurable subsets of Euclidean space. J. Fourier Anal. Appl., 16:813–839, 2010.
3. S. Mak and V.R. Joseph. Support points. Annals of Statistics, 46(6A):2562–2592, 2018.
4. L. Pronzato and A.A. Zhigljavsky. Bayesian quadrature, energy minimization and space-filling design. SIAM/ASA J. Uncertainty Quantification, 8(3):959–1011, 2020.
5. S. Sejdinovic, B. Sriperumbudur, A. Gretton, and K. Fukumizu. Equivalence of distance-based and RKHS-based statistics in hypothesis testing. The Annals of Statistics, 41(5):2263–2291, 2013.
6. B.K. Sriperumbudur, A. Gretton, K. Fukumizu, B. Schölkopf, and G.R.G. Lanckriet. Hilbert space embeddings and metrics on probability measures. Journal of Machine Learning Research, 11:1517–1561, 2010.
7. M. Welling. Herding dynamical weights to learn. In Proc. 26th Annual International Conference on Machine Learning, pages 1121–1128, 2009.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Didier Clouteau (MSSMAT), Amélie Fau (LMT), Filippo Gatti (MSSMAT), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (DOTA), Fernando Lopez-Caballero (MSSMAT), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Toni Karvonen (University of Helsinki) — [slides]

Parameter estimation in Gaussian process regression for deterministic functions

In fields such as kriging, modelling of computer experiments, and probabilistic numerical computation, Gaussian process (GP) regression is used to interpolate deterministic functions which are observed without noise on compact sets. This talk reviews recent theoretical work on estimation of parameters (in particular via maximum likelihood) of the covariance kernel of the GP prior in such a setting, as well as the effect parameter estimation has on uncertainty quantification under model misspecification. We also discuss results on sample path properties of GPs that we use to characterise data-generating functions which resemble samples from a GP and to highlight the difference in assuming that the data are generated by some deterministic function or by a stochastic process. The results are based on the theory of reproducing kernel Hilbert spaces and function approximation in Sobolev spaces, which are briefly reviewed. Ref: DOI:10.1137/20M1315968, arXiv:2103.03169, arXiv:2110.02810.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Didier Clouteau (MSSMAT), Amélie Fau (LMT), Filippo Gatti (MSSMAT), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (DOTA), Fernando Lopez-Caballero (MSSMAT), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Thomas Santner (Ohio State University) — [slides]

Using Combined Physical and Computer Experiments to Solve Bioengineering Problems

Bioengineering seeks to solve problems at the confluence of Engineering and Biology. Classical Bioengineering applications concerned the engineering design, and analysis of the performance of prosthetic joints, such as hips and knees, in multiple operating environments. More recent Bioengineering applications are concerned with designing replacement tissues, and analyzing different treatments for joint tissue injuries. Finite element methods can be used to numerically approximate the stresses and strains in the human bone when prosthetic joints are implanted or when cushioning tissues such as menisci are damaged. Prediction methodology from the computer experiments literature can be used to approximate the stresses and strains for a wide variety of potential prosthetic designs, to study their performance in multiple environments, and to determine the sensitivity of the prosthetic designs to specific engineering and environmental inputs. This talk will provide an overview of two such projects and describe how computer experiment methodology, including calibration to cadaver data, was used to provide insight into their solution. Ref: DOI:doi.org/10.1007/978-1-4757-3799-8.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Didier Clouteau (MSSMAT), Amélie Fau (LMT), Filippo Gatti (MSSMAT), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (DOTA), Fernando Lopez-Caballero (MSSMAT), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

3–4 PM — Polina Kirichenko (New York University) — [slides]

Scaling Bayesian Deep Learning: Subspace Inference

Bayesian methods can provide full-predictive distributions and well-calibrated uncertainties in modern deep learning. The Bayesian approach is especially relevant in scientific and healthcare applications—where we wish to have reliable predictive distributions for decision making, and the facility to naturally incorporate domain expertise. With a Bayesian approach, we not only want to find a single point that optimizes a loss, but rather to integrate over a loss landscape to form a Bayesian model average. The geometric properties of the loss surface, rather than the specific locations of optima, therefore greatly influence the predictive distribution in a Bayesian procedure. By better understanding loss geometry, we can realize the significant benefits of Bayesian methods in modern deep learning, overcoming challenges of dimensionality. In this talk, I review work on Bayesian inference and loss geometry in modern deep learning, including challenges, new opportunities, and applications. Refs: arxiv.org:1505.05424, arxiv:1706.04599, arxiv:1609.04836, arxiv:1506.02142, stoclangevin_v6.pdf, arxiv:1612.01474, arxiv:1902.02476, arxiv:1907.07504

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Didier Clouteau (MSSMAT), Amélie Fau (LMT), Filippo Gatti (MSSMAT), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (DOTA), Fernando Lopez-Caballero (MSSMAT), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Elmar Plischke (T.U. Clausthal) — [slides]

Optimal-transport-based sensitivity measures and their computation

The theory of optimal transport and the use of Wasserstein distances are attracting increasing attention in statistics and machine learning. At the same time, the definition of sensitivity measures for multivariate responses is a topical research subject. This work examines the construction of probabilistic sensitivity measures using the theory of optimal transport. We obtain a new family of indicators that can deal with multivariate outputs. We test estimators based on alternative algorithmic approaches for computing optimal transport problems, showing promising results and fast execution times for resonable sample sizes. Joint work with E. Borgonovo & G. Savarè (Bocconi Univ.), A. Figalli (ETH Zürich) Ref: preprint + code snippets.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Didier Clouteau (MSSMAT), Amélie Fau (LMT), Filippo Gatti (MSSMAT), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (DOTA), Fernando Lopez-Caballero (MSSMAT), Didier Lucor (LISN), Emmanuel Vazquez (L2S). Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Iason Papaioannou (T.U. Munich) — [slides]

Reliability sensitivity analysis with FORM

This talk discusses reliability sensitivity analysis with the first-order reliability method (FORM). Classical sensitivity indices, which are often used to assess the influence of the input random variables on the probability of failure, are the FORM $\alpha$-factors. These factors are the directional cosines of the the most likely failure point in an underlying independent standard normal space and are obtained as by-products of the FORM analysis. The talk reviews a set of alternative reliability sensitivity indices and their estimation with FORM. Focus is put on variance-based reliability sensitivities that emerge from the variance decomposition of the indicator function of the failure event. The resulting first-order and total-effect reliability sensitivities can be estimated as a function of the FORM reliability indices and the $\alpha$-factors. The second part of the talk addresses decision-oriented sensitivities based on the concept of value of information. In particular, the indices associated with a decision related to the safety of an existing system are presented and their estimation with FORM is examined. The accuracy of the FORM approximations of the various sensitivities is demonstrated with numerical examples. Joint work with Daniel Straub. Ref: DOI:10.1016/j.ress.2021.107496 (preprint) and arxiv:2104.00986.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Andreas Fichtner (ETH Zürich) — [slides]

Probabilistic Full-Waveform Inversion

In the course of the past decade, full-waveform inversion has matured from a largely idealistic dream into a commonly applied method to image the internal structure of inaccessible bodies. Despite undeniable success, a major problem remains: The quantification of uncertainties in this often strongly nonlinear inverse problem. In this lecture, I will present a series of computational approaches that brings probabilistic full-waveform inversion with complete uncertainty quantification within reach: 1) Hamiltonian Monte Carlo sampling of the posterior probability density treats model parameters as particles that orbit through model space, obeying Hamilton’s equations from classical mechanics. The scaling properties of Hamiltonian Monte Carlo allow us to consider high-dimensional model spaces that often cannot be considered with more traditional, derivative-free sampling methods. 2) Autotuning based on limited-memory quasi-Newton methods provides nearly optimal mass matrices for Hamiltonian Monte Carlo, thereby largely removing laborious manual tuning. A factorised version of the L-BFGS algorithm, in particular, can increase the effective sample size by more than an order of magnitude. 3) Wavefield-adapted spectral-element meshes exploit prior knowledge on the geometry of wavefields. Such prior knowledge is frequently available for media that are smooth relative to the minimum wavelength. Wavefield-adapted meshes have the potential to drastically reduce the number of elements, leading to a computational forward modelling cost that makes Monte Carlo sampling possible. Joint work with Lars Gebraad & Christian Boehm. Ref: DOI:10.1029/2019JB018428.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Adrien Touboul (IRT SystemX & CERMICS) — [slides]

Uncertainty Quantification in graphs of functions through sample reweighting

The needs for multidisciplinary simulations in the design of complex industrial systems motivate the development of Uncertainty Quantification and Sensitivity Analysis methods that are compatible with disciplinary autonomy. This presentation focuses on decomposition methods based on sample reweighting. The design process is modeled by a graph, whose nodes are simulation codes and edges are exchanges of variables. The first part of this presentation is dedicated to the study of one particular reweighting method, based on the minimization of a Wasserstein distance. An explicit expression of the weights is exhibited in terms of Nearest Neighbors and some consistency results and rates of convergence are derived. The second part is dedicated to the general propagation of the weights in directed acyclic graphs, inspired from an existing algorithm of Amaral, Allaire & Willcox (2014). A general framework is developed to characterize the consistency of the global algorithm in terms of local weighting condition at each node. We observe that some weighting schemes can be obtained naturally from nonparametric linear regressions and linear smoothers. An interesting equivalence with some already existing tools in the literature permits to simplify the numerical computations part. The final algorithm does not require that the simulation codes have to be run at the same time or in a specific order. Hence, it allows for disciplinary autonomy. Joint work with Julien Reygner. Ref: hal-02968059.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Clément Gauchy (CEA & École polytechnique) — [slides]

An information geometry approach for robustness analysis in uncertainty quantification of computer codes

Robustness analysis is an emerging field in the uncertainty quantification domain. It involves analyzing the response of a computer model—which has inputs whose exact values are unknown—to the perturbation of one or several of its input distributions. Practical robustness analysis methods therefore require a coherent methodology for perturbing distributions; we present here one such rigorous method, based on the Fisher distance on manifolds of probability distributions. Further, we provide a numerical method to calculate perturbed densities in practice which comes from Lagrangian mechanics and involves solving a system of ordinary differential equations. The method introduced for perturbations is then used to compute quantile-related robustness indices. We illustrate these « perturbed-law based » indices on several numerical models. We also apply our methods to an industrial setting: the simulation of a loss of coolant accident in a nuclear reactor, where several dozen of the model’s physical parameters are not known exactly, and where limited knowledge on their distributions is available. Joint work with Jérôme Stenger, Roman Sueur et Bertrand Iooss. Refs: DOI:10.1080/00401706.2021.1905072.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Clément Gauchy (CEA & École polytechnique) — [slides]

An information geometry approach for robustness analysis in uncertainty quantification of computer codes

Robustness analysis is an emerging field in the uncertainty quantification domain. It involves analyzing the response of a computer model—which has inputs whose exact values are unknown—to the perturbation of one or several of its input distributions. Practical robustness analysis methods therefore require a coherent methodology for perturbing distributions; we present here one such rigorous method, based on the Fisher distance on manifolds of probability distributions. Further, we provide a numerical method to calculate perturbed densities in practice which comes from Lagrangian mechanics and involves solving a system of ordinary differential equations. The method introduced for perturbations is then used to compute quantile-related robustness indices. We illustrate these « perturbed-law based » indices on several numerical models. We also apply our methods to an industrial setting: the simulation of a loss of coolant accident in a nuclear reactor, where several dozen of the model’s physical parameters are not known exactly, and where limited knowledge on their distributions is available. Joint work with Jérôme Stenger, Roman Sueur et Bertrand Iooss. Refs: DOI:10.1080/00401706.2021.1905072.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Stefano Mariani (DICA @ Politecnico di Milano) — [slides]

Online damage detection and model updating via proper orthogonal decomposition and recursive Bayesian filters

An approach based on the synergistic use of proper orthogonal decomposition (POD) and Kalman filtering is proposed for the online health monitoring of damaged structures. The reduced-order model of the structure is obtained during the initial training stage of monitoring; afterward, effective estimations of structural damage are provided online by tracking the evolution in time of stiffness parameters and projection bases handled in the model order reduction procedure. Such tracking is accomplished via two Kalman filters: a first one to deal with the time evolution of a joint state vector, gathering the reduced-order state and the stiffness terms degraded by damage; a second one to deal with the update of the reduced-order model in case of damage evolution. Both filters exploit the information conveyed by measurements of the structural response to the external excitations. Focusing on multi-story shear building, the capability and performance of the proposed approach are assessed in terms of tracked variation of the stiffness terms, identified damage location and speed-up of the whole health monitoring procedure. Joint work with Saeed Eftekhar Azam, Giovanni Capellari, Francesco Caimmi. Refs: 10.1016/j.engstruct.2017.12.031, 10.1007/s11071-017-3530-1, 10.3390/s16010002, 10.1504/IJSMSS.2015.078355, 10.1016/j.engstruct.2013.04.004.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Chris Oates (Newcastle University and Alan Turing Inst.) — [slides]

Optimal Thinning of MCMC Output

There is a recent trend in computational statistics to move away from sampling methods and towards optimisation methods for posterior approximation. These include discrepancy minimisation, gradient flows and control functionals—all of which have the potential to deliver faster convergence than a Monte Carlo method. In this talk we will see how ideas from discrepancy minimisation can be applied to the problem of optimal thinning of MCMC output. Joint work with Marina Riabiz, Wilson Chen, Jon Cockayne, Pawel Swietach, Steve Niederer, Lester Mackey. Ref: arXiv:2005.03952 and http://stein-thinning.org.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Julien Pelamatti (EDF R&D) — [slides]

Bayesian optimization of variable-size design space problems

Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables. Additionally, complex system design problems occasionally present a variable-size design space. This results in an optimization problem for which the search space varies dynamically (with respect to both number and type of variables) along the optimization process as a function of the values of specific discrete decision variables. Similarly, the number and type of constraints can vary as well. In this paper, two alternative Bayesian optimization-based approaches are proposed in order to solve this type of optimization problems. The first one consists of a budget allocation strategy allowing to focus the computational budget on the most promising design sub-spaces. The second approach, instead, is based on the definition of a kernel function allowing to compute the covariance between samples characterized by partially different sets of variables. The results obtained on analytical and engineering related test-cases show a faster and more consistent convergence of both proposed methods with respect to the standard approaches. Joint work with Loic Brevault (ONERA), Mathieu Balesdent (ONERA), El-Ghazali Talbi (Inria Lille), Yannick Guerin (CNES). Ref: arXiv:2003.03300.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Amaya Nogales Gómez (I3S, Sophia Antipolis) — [slides]

Incremental space-filling design based on coverings and spacings: improving upon low discrepancy sequences

The paper addresses the problem of defining families of ordered sequences {x_i} i∈N of elements of a compact subset X of R^d whose prefixes X_n = {x_i} i=1, …, n, for all orders n, have good space-filling properties as measured by the dispersion (covering radius) criterion. Our ultimate aim is the definition of incremental algorithms that generate sequences X_n with small optimality gap, i.e., with a small increase in the maximum distance between points of X and the elements of X_n with respect to the optimal solution X_n. The paper is a first step in this direction, presenting incremental design algorithms with proven optimality bound with respect to one-parameter families of criteria based on coverings and spacings that both converge to dispersion for large values of their parameter. Joint work with Luc Pronzato and Maria-Joao Rendas. Ref: hal-02987983.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Victor Picheny (Secondmind)

Bayesian optimisation: ablation study, global performance assessment and improvements based on trust regions

Bayesian Optimisation algorithms (BO) are global optimisation methods that iterate by constructing and using conditional Gaussian processes (GP). It is a common claim that BO is state-of-the-art for costly functions. However, this claim is weakly supported by experimental evidence, as BO is most often compared to itself, rather than to algorithms of different nature. In this work, we study the performance of BO within the well-known COmparing Continuous Optimizers benchmark (COCO). We first analyse the sensitivity of BO to its own parameters, enabling us to answer general questions regarding the choice of the GP kernel or its trend, the initial GP budget, and the suboptimisation of the acquisition function. Then, we study on which function class and dimension BO is relevant when compared to state-of-the-art optimisers for expensive functions. The second part of this talk describes a new BO algorithm to improve scalability with dimension, called TREGO (trust-region-like efficient global optimisation). TREGO alternates between regular BO steps and local steps within a trust region. By following a classical scheme for the trust region (based on a sufficient decrease condition), we demonstrate that our algorithm enjoys strong global convergence properties, while departing from EGO only for a subset of optimization steps. The COCO benchmark experiments reveal that TREGO consistently outperforms EGO and closes the performance gap with other state-of-the-art algorithms in conditions (high budget and dimension) for which BO was struggling to compete previously. Joint work Youssef Diouane, Rodolphe Le Riche, Alexandre Scotto Di Perrotolo. Ref: arXiv:2101.06808 & DiceOptim.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Amandine Marrel (CEA & IMT)

ICSCREAM methodology for the Identification of penalizing Configurations using SCREening And Metamodel — Application to high-dimensional thermal-hydraulic numerical experiments

In the framework of risk assessment in nuclear accident analysis, best-estimate computer codes are used to estimate safety margins. Several inputs of the code can be uncertain, due to a lack of knowledge but also to the particular choice of accidental scenario being considered. The objective of this work is to identify the most penalizing (or critical) configurations of several input parameters (called “scenario inputs”), independently of the uncertainty of the other inputs. Critical configurations of the scenario inputs correspond to high values of the code output Y, defined here by exceeding the 90%-quantile. However, thermal-hydraulic codes are too CPU-time expensive to be directly used to propagate the input uncertainties and solve the inversion problem. The adopted solution consists in fitting the code output by a metamodel, built from a reduced number of code simulations. When the number of input parameters is very large (e.g., around a hundred here), the metamodel building remains a challenge. To overcome this, we have developed a methodology, called ICSCREAM for Identification of penalizing Configurations using SCREening And Metamodel. Applied from a Monte Carlo sample of code simulations, the ICSCREAM methodology judiciously combines a step of SA to identify and rank the main influential inputs and to reduce the dimension, before building a Gaussian process (GP) metamodel. SA relies on new statistical independence tests that aggregate information of global and target Hilbert-Schmidt independence criteria. The GP is then efficiently built with a sequential process, where the inputs are taken into account in a more or less fine way, according to their supposed influence. Finally, the GP metamodel is intensively used to estimate the conditional probabilities of Y exceeding the critical value, according to each inputs to be penalized. Accurate uncertainty propagation, not feasible with the computational costly model, become therefore accessible with the ICSCREAM methodology. Joint work with Bertrand Iooss (EDF R&D & IMT) and Vincent Chabridon (EDF R&D). Ref: hal-02535146.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

2–3 PM — Clémentine Prieur (LJK, Univ. Grenoble Alpes)

Global sensitivity analysis for models described by stochastic differential equations

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest. One of the statistical tools used to quantify the influence of each input variable on the quantity of interest are the Sobol’ sensitivity indices. In this paper, we consider stochastic models described by stochastic differential equations (SDE). We focus the study on mean quantities, defined as the expectation with respect to the Wiener measure of a quantity of interest related to the solution of the SDE itself. Our approach is based on a Feynman-Kac representation of the quantity of interest, from which we get a parametrized partial differential equation (PDE) representation of our initial problem. We then handle the uncertainty on the parametrized PDE using polynomial chaos expansion and a stochastic Galerkin projection. Joint work with Pierre Étoré, Dang Khoi Pham & Long Li. Ref: hal-01926919.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

14h–15h — Cédric Travelletti (University of Bern)

Implicit Update for Large-Scale Inversion under GP prior

We present an almost matrix-free update method for posterior Gaussian process distributions under sequential observations of linear functionals. By introducing a novel implicit representation of the posterior covariance matrix, we are able to extract posterior covariance information on large grids and to provide a framework for sequential data assimilation when covariance matrices cannot fit in memory. This is useful in Bayesian linear inverse problems with Gaussian priors, where the matrices involved grow quadratically in the number of elements in the discretization grid, creating memory bottlenecks when inverting on fine-grained discretizations. We illustrate our method by applying it to an excursion set recovery task arising from a gravimetric inverse problem on Stromboli volcano. In this setting, we demonstrate computation and sequential updating of exact posterior mean and covariance at resolutions finer than what state-of-the-art techniques can handle and showcase how the proposed framework enables implementing large-scale probabilistic excursion set estimation and also deriving efficient experimental design strategies tailored to this goal. Joint work with David Ginsbourger (Univ. Bern) and Niklas Linde (Univ. Lausanne). Ref: Volcapy (github).

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

14h–15h — Bojana Rosic (University of Twente, Netherlands)

Inverse methods for damage estimation in concrete given small data sets

One of the main issues in material science is estimation of the constitutive laws given experimental data that may come in different forms ranging from the microscopic images to the macroscopic data collected by strain gauges for example. As data are often heterogeneous, of multi-scale/temporal nature, possibly ambiguous and of low quality due to missing values, the process of learning is often requiring the careful application of existing or design of new data fusion algorithms that are bounded to small data sets. In this talk will be presented the computationally efficient Bayesian algorithms for the damage estimation. In particular, the special attention will be paid to damage model estimation by using both classical uncertainty quantification as well as machine/deep learning approaches. Joint work with (alphabetical order) X. Chapeleau, P.-E. Charbonnel, L.-M. Cottineau, L. De Lorenzis, A. Ibrahimbegovic, V. Le Corvec, H.G. Matthies, E. Merliot, M.S. Sarfaraz, D. Siegert, R. Vidal, J. Waeytens and T. Wu. Refs: hal-01379214, arXiv:1909.07209, DOI:10.1007/s00466-020-01942-x, arXiv:1912.03108.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

14h–15h — Álvaro Rollón de Pinedo (EDF R&D and Université Grenoble Alpes)

Functional outlier detection applied to nuclear transient simulation analysis

The ever increasing recording and storing capabilities of industrial systems provide a large amount of physical data that can be exploited by engineers. These data may take the form of functions, usually a one-dimensional function of time, but eventually as a multidimensional function of space and time. Finding the subsets of objects that behave abnormally in them is a goal that can prove to be useful in order to avoid spurious results, simulations that do not reproduce certain physical phenomena as expected, or extreme physical events and domains. In the context of nuclear transient simulations, safety reports mostly focus on the study of some scalar parameters (safety criteria), supposed to guarantee the safety of an installation during an accidental transient as long as they do not surpass a previously established threshold. Nevertheless, the state- of-the-art simulations codes (called Best Estimate) provide a much richer and complex information, which can be better taken advantage of through the identification outlying simulations amongst those generated as outputs.   The goal of this talk is to introduce the functional outlier detection domain, highlighting its interest in industrial settings, as well as to present our detection technique and the conclusions on the physical analysis of nuclear transients that can be obtained from its use. Joint work with Mathieu Couplet, Bertrand Iooss, Nathalie Marie, Amandine Marrel, Elsa Merle and Roman Sueur. Reference: hal-02965504.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

14h–15h — Eyke Hüllermeier (Paderborn University, Germany) — [slides]

Aleatoric and Epistemic Uncertainty in Machine Learning: An Ensemble-based Approach

Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last couple of years. This talk will address the question of how to distinguish between two important types of uncertainty, often refereed to as aleatoric and epistemic, in the setting of supervised learning, and how to quantify these uncertainties in terms of suitable numerical measures. Roughly speaking, while aleatoric uncertainty is due to inherent randomness, epistemic uncertainty is caused by a lack of knowledge. As a concrete approach for uncertainty quantification in machine learning, the use of ensemble learning methods will be discussed. Joint work with S. Destercke, V.-L. Nguyen, M. H. Shaker & W. Waegeman. References: arXiv:1910.09457, arXiv:1909.00218, arXiv:2001.00893.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

14h–15h — Luc Bonnet (ONERA & MSSMAT) — [slides]

The expected performance of a system can generally differ from its operational performance due to the variability of some parameters. Optimal Uncertainty Quantification is a powerful mathematical tool that can be used to rigorously bound the probability of exceeding a given performance threshold for uncertain operational conditions or system characteristics. Metamodeling is at the heart of this research framework. In this perspective, Kernel Flow, a recent method to obtain a metamodel by kriging developed by Owhadi & Yoo, will be presented. The results obtained will be illustrated by examples in numerical and experimental aerodynamics. Joint work with Eric Savin and Houman Owhadi. References: 10.1016/j.jcp.2019.03.040, 10.1137/10080782X & 10.3390/a13080196.

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

14h–15h — Nicolas Bousquet (EDF R&D)

Well-posed stochastic inversion in uncertainty quantification, with links with sensitivity analysis

Stochastic inversion problems are typically encountered when it is wanted to quantify the uncertainty affecting the inputs of computer models. They consist in estimating input distributions from noisy, observable outputs, and such problems are increasingly examined in Bayesian contexts where the targeted inputs are affected by a mixture of aleatory and epistemic uncertainties. While they are characterized by identifiability conditions, well-posedness constraints of « signal to noise » have to be took into account within the definition of the model, prior to inference. In addition to numeric conditioning notions and regularization techniques used in inverse problems, we propose and investigate an interpretation of well-posedness, in the context of parametric uncertainty quantification and global sensitivity analysis, based on the degradation of Fisher information. It offers an explicitation of such prior constraints considering linear or linearizable operators, this linearization being either local (based on differentiability) or variational. Simulated experiments indicate that, when injected into the modeling process, these constraints can limit the influence of measurement or process noise on the estimation of the input distribution, and let hope for future extensions in a full non-linear framework, for example through the use of linear Gaussian mixtures.​

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

14h–15h — Sebastian Schöps (TU Darmstadt)

Uncertainty Quantification for Maxwell’s eigenproblem based on isogeometric analysis and mode tracking

Superconducting cavities are used in particle accelerators, e.g. at DESY in Hamburg, Germany. Their resonating electromagnetic field is commonly characterised by eigenmodes and eigenvalues which are very sensitive to small geometry deformations. This presentation proposes an uncertainty quantification workflow based on a Karhunen–Loève expansion of the manufacturing imperfections and eigenvalue tracking based on algebraic and geometric homotopies. Joint work with Niklas Georg, Wolfgang Ackermanna, Jacopo Corno. Reference: DOI:10.1016/j.cma.2019.03.002 (arxiv:1802.02978).

Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Bertrand Iooss (EDF R&D).

Practical details: the seminar will be held online using Microsoft Teams. If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account). You will find the link to the seminar on the « General » UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from you web browser or using the « fat client », which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.

14h — Alexandre Janon (Laboratoire de Mathématique d’Orsay) — [slides]

Part 1: Consistency of Sobol indices with respect to stochastic ordering of input parameters

In the past decade, Sobol’s variance decomposition have been used as a tool – among others – in risk management. We show some links between global sensitivity analysis and stochastic ordering theories. This gives an argument in favor of using Sobol’s indices in uncertainty quantification, as one indicator among others. Reference: https://doi.org/10.1051/ps/2018001 (hal-01026373)

Part 2: Global optimization using Sobol indices

We propose and assess a new global (derivative-free) optimization algorithm, inspired by the LIPO algorithm, which uses variance-based sensitivity analysis (Sobol indices) to reduce the number of calls to the objective function. This method should be efficient to optimize costly functions satisfying the sparsity-of-effects principle. Reference: hal-02154121

15h — Pierre Barbillon (MIA Paris) — [slides]

Sensitivity analysis of spatio-temporal models describing nitrogen transfers, transformations and losses at the landscape scale

Modelling complex systems such as agroecosystems often requires the quantification of a large number of input factors. Sensitivity analyses are useful to determine the appropriate spatial and temporal resolution of models and to reduce the number of factors to be measured or estimated accurately. Comprehensive spatial and temporal sensitivity analyses were applied to the NitroScape model, a deterministic spatially distributed model describing nitrogen transfers and transformations in rural landscapes. Simulations were led on a theoretical landscape that represented five years of intensive farm management and covering an area of 3km2. Cluster analyses were applied to summarize the results of the sensitivity analysis on the ensemble of model outputs.The methodology we applied is useful to synthesize sensitivity analyses of models with multiple space-time input and output variables and could be ported to other models than NitroScape. Reference: https://doi.org/10.1016/j.envsoft.2018.09.010 (arXiv:1709.08608)

Organizers: Julien Bect (L2S) and Bertrand Iooss (EDF R&D). No registration is needed, but an email would be appreciated if you intend to come.