UQSay #59

Date : 11/05/2023
Catégorie(s) : ,
Lieu : Online (Teams)

The fifty-nineth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, May 11, 2023.

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


  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.