UQSay #103

The hundred and third UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, November 5, 2026.

2–3 PM — Clémentine Chazal (CREST - ENSAE)

A Computable Measure of Suboptimality for Entropy-Regularised Variational Objectives

Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an explicit unnormalised density for the target. To mitigate this difficulty, we introduce a novel measure of sub-optimality called gradient discrepancy, and in particular a kernel gradient discrepancy (KGD) that can be explicitly computed. In the standard Bayesian context, KGD coincides with the kernel Stein discrepancy (KSD), and we obtain a novel characterisation of KSD as measuring the size of a variational gradient. Outside this familiar setting, KGD enables novel sampling algorithms to be developed and compared, even when unnormalised densities cannot be obtained. To illustrate this point several novel algorithms are proposed and studied, including a natural generalisation of Stein variational gradient descent, with applications to mean-field neural networks and predictively oriented posteriors presented. On the theoretical side, our principal contribution is to establish sufficient conditions for desirable properties of KGD, such as continuity and convergence control.

References:

• A Computable Measure of Suboptimality for Entropy-Regularised Variational Objectives, 2025

Joint work with Heishiro Kanagawa & Zheyang Shen (Newcastle University) & Anna Korba (CREST-ENSAE) & Chris J. Oates (Newcastle University - Alan Turing Institute).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Oindrila Kanjilal (LMPS), 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.

UQSay #102

The hundred and second UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, October 22, 2026.

2–3 PM — Rui Tuo (Department of Industrial and Systems Engineering, Texas A&M University) — [slides]

Statistical Validation of Computer Models: Global and Subdomain Hypothesis Testing

Computer simulations play an important role in scientific discovery and engineering innovation. Reliable computer models enable virtual experimentation that reduces the need for costly and time-consuming physical testing. However, the credibility of such models hinges on rigorous statistical validation against real-world data. This paper develops a formal frequentist framework for both global and subdomain validation of computer models. We propose the Fourier Maximum Modulus Test (FMMT), which leverages kernel ridge regression (KRR) to estimate the discrepancy between the computer model and the physical process, followed by a frequency-domain test based on weighted generalized Fourier coefficients. The theoretical analysis establishes the asymptotic normality of these coefficients, allowing for closed-form p-values. Simulation studies and a shear-layer experiment demonstrate that FMMT achieves high power, accurate Type I error control, and strong sensitivity to localized discrepancies.

References:

• Statistical Validation of Computer Models: Global and Subdomain Hypothesis Testing, 2026

Joint work with Chaoan Li & Xianyang Zhang (Department of Statistics, Texas A&M University).

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Oindrila Kanjilal (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.

UQSay #101

The hundred and first UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, June 11, 2026.

2–3 PM — Zonghao Chen (FSML, University College London) — [slides]

Stationary MMD points

Approximation of a target probability distribution using a finite set of points is a problem of fundamental importance in numerical integration. Several authors have proposed to select points by minimising a maximum mean discrepancy (MMD), but the non-convexity of this objective typically precludes global minimisation. Instead, we consider the concept of stationary points of the MMD which, in contrast to points globally minimising the MMD, can be accurately computed. Our main contributions are two-fold and theoretical in nature. We first prove the (perhaps surprising) result that, for integrands in the associated reproducing kernel Hilbert space, the numerical integration error of stationary MMD points vanishes faster than the MMD. Motivated by this super-convergence property, we consider MMD gradient flows as a practical strategy for computing stationary points of the MMD. We then prove that MMD gradient flow can indeed compute stationary MMD points, based on a refined convergence analysis that establishes a novel non-asymptotic finite-particle error bound.

References:

• Stationary MMD points, 2025

Joint work with Toni Karvonen (Lappeenranta–Lahti University of Technology) & Heishiro Kanagawa (Newcastle University) & François-Xavier Briol (UCL) & Chris Oates (Newcastle University).

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.

UQSay #100

The one hundredth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, May 28, 2026.

2–3 PM — Julien Bect & Xujia Zhu ( L2S, CentraleSupélec)

(Goal-Oriented) Global Sensitivity Analysis Revisited:The Mystery of the Camembert Slices

Sensitivity analysis plays a critical role in uncertainty quantification, aiming to characterize how uncertainty in model inputs propagates through computational models or experiments to the outputs. In contrast to local approaches, global methods account for variability over the entire input space, providing a more thorough description of input-output relationships. A wide range of global sensitivity indices has been proposed over the past decades, particularly to define so-called closed sensitivity indices , which quantify the joint contribution of a group (or coalition) of input variables.

From closed indices, one can easily derive first-order (main) effects and higher-order interaction effects. A desirable property in this setting is the non-negativity of the resulting sensitivity indices, which yields an interpretable decomposition of the total uncertainty, much like a pie chart---or ``Camembert'' diagram, as it is sometimes called in French---partitions a whole into non-overlapping contributions. However, this property does not hold in general. In fact, beyond the well-known case of variance-based (Sobol') sensitivity indices, to the best of our knowledge, only two frameworks ensure non-negative higher-order indices, both of them discovered quite recently by Da Veiga [1]: the first one relies on the expected Maximum Mean Discrepancy (MMD) between the conditional and the marginal distribution, while the second one leverages the Hilbert--Schmidt Independence Criterion (HSIC) in combination with specific (ANOVA) kernels.

In this talk, we first review three constructions of closed sensitivity indices available in the literature, in relation with the key notion of uncertainty functional [2]. Then we present a unified framework [3] that clarifies the common mechanism at work in the two classes of indices proposed by Da Veiga. At the heart of this framework resides a new avatar of the Sobol'-Hoeffding decomposition, also known as the functional ANOVA decomposition. Finally, we discuss several open questions and directions for future research, in particular regarding general necessary and sufficient conditions for higher-order indices to be non-negative.

References:

• [1] Kernel-based ANOVA decomposition and Shapley effects—application to global sensitivity analysis, 2021
• [2] Uncertainty functionals revisited: Concavity and Jensen’s inequality, 2026
• [3] On non-negative coalitional decompositions in global sensitivity analysis, in preparation, 2026

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.

UQSay #99

The ninety-ninth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, May 7, 2026.

2–3 PM — Donatien Rossat ( EDF R&D) — [slides]

Information Geometry-based Robust Bayesian Analysis

Bayesian inference provides a comprehensive framework for quantifying epistemic uncertainties, and updating them from new information. It relies on updating a so-called prior distribution, which summarizes the level of knowledge about some input parameters. In this work, we introduce a novel sensitivity analysis method to quantify the influence of prior distributions on Bayesian inference outcomes. We define perturbed-law-based sensitivity indices (PLI), which measure the effect of uncertainties in prior specification through controlled perturbations of a reference prior. These perturbations are constructed using the Fisher distance from information geometry, enabling a consistent exploration of a wide range of deviations beyond infinitesimal changes. We further show that these indices can be reformulated as relative variations of rare event probabilities, allowing efficient computation using existing reliability methods. The proposed approach is illustrated on Bayesian inverse problems of varying complexity. Results demonstrate its ability to identify parameters for which prior choices significantly impact Bayesian inference results, while remaining applicable to nonlinear and high-dimensional settings.

References:

• Information Geometry-based Robust Bayesian Analysis, International Journal for Uncertainty Quantification , 2026

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.

UQSay #98

The ninety-eighth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, April 9, 2026.

2–3 PM — Lucia Clarotto (MIA Paris-Saclay, AgroParisTech - Geolearning Chair) — [slides]

Prediction of spatio-temporal Gaussian processes by advection-diffusion stochastic partial differential equations

In the task of predicting spatio-temporal fields in environmental science using statistical methods, introducing statistical models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest. Large space–time datasets call for new numerical methods to efficiently process them. The Stochastic Partial Differential Equation (SPDE) approach has proven to be effective for the estimation and the prediction in a spatial context. We present here the advection–diffusion SPDE with first–order derivative in time which defines a large class of nonseparable spatio-temporal models, both on Euclidean spaces and Riemamnnian manifolds. A Gaussian Markov random field approximation of the solution to the SPDE is built by discretizing the temporal derivative with a finite difference method and by solving the spatial SPDE with a finite element method at each time step. Computationally efficient methods are proposed to estimate the parameters of the SPDE and to predict the spatio-temporal field by kriging, as well as to perform conditional simulations. The approach is applied to datasets of solar radiation and atmospheric aerosol optical depth across the Earth’s surface.

References:

• The SPDE approach for spatio-temporal datasets with advection and diffusion, Spatial Statistics, 2024
• Prediction of spatio-temporal data on meshed surfaces using advection-diffusion SPDEs, 2025

Joint work with Denis Allard (INRAE) & Nicolas Desassis & Mike Pereira & Thomas Romary (Mines 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.

UQSay #97

The ninety-seventh UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, March 26, 2026.

2–3 PM — Anthony Quintin (CEA DIF)

Optimal experimental designs based on the cross-entropy method for planning fracture toughness tests

Nuclear reactor pressure vessels undergo progressive embrittlement under neutron irradiation, monitored through the Master Curve theory which estimates a reference temperature T0. The core challenge is obtaining a reliable estimate of T0 from a very limited number of specimens. The work pursues two objectives. First, developing a numerical twin of fracture toughness test campaigns based on finite element simulations coupled with a Beremin model calibrated via Bayesian inference. Second, building a decision-making tool to optimize experimental planning within the framework of Bayesian Optimal Experimental Design, which seeks to determine the experimental conditions maximizing the information gained from a limited number of observations.

To this end, the approach relies on a Bayesian optimization method aimed at identifying test temperature sequences that minimize uncertainty on T0. The problem is formulated as a constrained combinatorial optimization, where the criterion to maximize is an expected information gain (entropy). Temperature sequences are modeled as homogeneous first-order discrete-time Markov chains, whose transition matrix is optimized via the Cross-Entropy Method. The resulting method yields a transition matrix that serves as a directly interpretable sequential decision rule. The proposed methodology is inherently general and transferable to any material and to a broad range of experimental testing frameworks where observations are limited and acquisition costs are high.

References:

• Plans d'expériences d'essais optimaux, 2025
• Uncertainty quantification of the reference temperature T0 of 16MND5 steel from experimental and numerical fracture toughness tests, 2025

Joint work with Jean Marc Bourinet & Cécile Mattrand (SIGMA Clermont) & Rudy Chocat (CEA Saclay) & Tom Petit (CEA Gramat)

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.