UQSay: UQ, DACE & related topics @ Paris-Saclay

UQSay is a series of seminars on the broad area of Uncertainty Quantification (UQ) and related topics (Read more…), organized by L2S, MSSMAT, LMT and EDF R&D.

Upcoming seminars

See https://www.uqsay.org/upcoming/.

All seminars

UQSay #24

The twenty-fourth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, February 18, 2021.

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.

UQSay #23

The twenty-third UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, February 4, 2021.

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).

UQSay #22

The twenty-second UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, January 21, 2021.

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).

UQSay #20

The twentieth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, December 17, 2020.

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).

UQSay #19

The nineteenth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, December 3, 2020.

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).

UQSay #18

The eighteenth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, November 19, 2020.

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).

UQSay #17

The seventeenth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, November 5, 2020.

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).

UQSay #16

The sixteenth UQSay seminar on Uncertainty Quantification and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, October 22, 2020.

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).

UQSay #15

The fifteenth UQSay seminar on Uncertainty Quantification and related topics, organized by L2S, MSSMAT, and EDF R&D, will take place online on Thursday afternoon, October 8, 2020.

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).

UQSay #14

The fourteenth UQSay seminar on Uncertainty Quantification and related topics, organized by L2S, MSSMAT, and EDF R&D, will take place online on Thursday afternoon, September 24, 2020.

14h–15h — Amélie Fau (LMT, ENS Paris-Saclay)

Alternative strategies for adaptive sampling for kriging metamodels

A large variety of strategies have been proposed in the literature to offer optimal dataset for kriging metamodels. Even though adaptive schemes guarantee convergence and improvement of estimation accuracy for instance for Galerkin approaches at least in a goal-oriented sense, using usual adaptive sampling schemes for kriging metamodels might be detrimental, worsing prediction results compared to one-shot sampling techniques. The goal of this seminar is to share our experience on cases leading to this disvantageous behavior. Besides, problems leading to beneficial behavior will be discussed to highlight criteria for deciding about cases of interest for which adaptive sampling strategies are highly promising.

Joint work with Jan Fuhg & Udo Nackenhorst (Leibniz Universität, Hannover).

Reference: DOI:10.1007/s11831-020-09474-6.

Organizers: 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.

UQSay #13

The thirteenth UQSay seminar on Uncertainty Quantification and related topics, organized by L2S, MSSMAT, and EDF R&D, will take place online on Thursday afternoon, September 10, 2020.

14h–15h — Balázs Kégl (Noah’s Ark Lab, Huawei Paris) — [slides]

DARMDN: Deep autoregressive mixture density nets for dynamical system modelling

Unlike computers, physical engineering systems (such as data center cooling or wireless network control) do not get faster with time. This is arguably one of the main reasons why recent beautiful advances in deep reinforcement learning (RL) stay mostly in the realm of simulated worlds and do not immediately translate to practical success in the real world. In order to make the best use of the small data sets these systems generate, we develop data-driven neural simulators to model the system and apply model-based control to optimize them. In this talk I will present the first step of this research agenda, a new versatile system modelling tool called deep autoregressive mixture density net (DARMDN – pronounced darm-dee-en). We argue that the performance of model-based reinforcement learning is partly limited by the approximation capacity of the currently used conditional density models and show how DARMDN alleviates these limitations. The model, combined with a random shooting controller, establishes a new state of the art on the popular Acrobot benchmark. Our most interesting and counter-intuitive finding is that the “sincos” Acrobot system which requires no multimodal posterior predictives, can be solved with a deterministic model, but only if it is trained as a probabilistic model. A deterministic model that is trained to minimize MSE leads to prediction error accumulation.

Joint work with Gabriel Hurtado and Albert Thomas.

Organizers: 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.

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

UQSay #07

The seventh UQSay seminar on Uncertainty Quantification and related topics, organized by L2S and MSSMAT, will take place on Thursday afternoon, January 16, 2020, at CentraleSupelec Paris-Saclay (Eiffel building, amphi III).

We will have two talks: 14h — Bertrand Iooss (EDF R&D / PRISME dept.) — [slides]

Iterative estimation in uncertainty and sensitivity analysis

While building and using numerical simulation models, uncertainty and sensitivity analysis are invaluable tools. In engineering studies, numerical model users and modellers have shown high interest in these techniques that require to run many times the simulation model with different values of the model inputs in order to compute statistical quantities of interest (QoI, i.e. mean, variance, quantiles, sensitivity indices…). In this talk we will focus on new issues relative to large scale numerical systems that simulate complex spatial and temporal evolutions. Indeed, the current practice consists in the storage of all the simulation results. Such a storage becoming quickly overwhelming, with the associated long read time that makes cpu time consuming the estimation of the QoI. One solution consists in avoiding this storage and in computing QoI on the fly (also called in-situ). It turns the problem to considering problems of iterative statistical estimation. The general mathematical and computational issues will be posed, and a particular attention will be paid to the estimation of quantiles (via an adaptation of the Robbins-Monro algorithm) and variance-based sensitivity indices (the so-called Sobol’ indices).

Joint work with Yvan Fournier (EDF), Bruno Raffin (INRIA), Alejandro Ribés (EDF), Théophile Terraz (INRIA).

UQSay #03

The third UQSay seminar, organized by L2S and EDF R&D, will take place on Thursday afternoon, June 13, 2019, at CentraleSupelec Paris-Saclay (Eiffel building, amphi V). We will have two talks:

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.

UQSay #01

The first UQSay seminar, organized by L2S, will take place in the afternoon of March 21, 2019, at CentraleSupelec Paris-Saclay (Eiffel building, amphi IV). We will have two talks:

14h – Mickaël Binois (INRIA Sophia-Antipolis) [slides]

Heteroskedastic Gaussian processes for simulation experiments

An increasing number of time-consuming simulators exhibit a complex noise structure that depends on the inputs. To conduct studies with limited budgets of evaluations, new surrogate methods are required to model simultaneously the mean and variance fields. To this end, we present recent advances in Gaussian process modeling with input-dependent noise. First, we describe a simple, yet efficient, joint modeling framework that rely on replication for both speed and accuracy. Then we tackle the issue of leveraging replication and exploration in a sequential manner for various goals, such as obtaining a globally accurate model, for optimization, contour finding, and active subspace estimation. We illustrate these on applications coming from epidemiology and inventory management.

Ref : https://arxiv.org/abs/1710.03206.

15h – François Bachoc (IMT, Toulouse) [slides]

Gaussian process regression model for distribution inputs

Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. In this paper, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provide a family of positive definite kernels built using transportation based distances. We provide asymptotic results for covariance function estimation and prediction. We also provide numerical comparisons with other forecast methods based on distribution inputs.

Ref : https://arxiv.org/abs/1701.09055.

Organizers : Julien Bect (L2S) and Emmanuel Vazquez (L2S).

No registration is needed, but an email would be appreciated if you intend to come.