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)

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.

UQSay #96

The ninety-sixth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, March 12, 2026.

2–3 PM — Richard Everitt (Department of Statistics, University of Warwick) — [slides]

Improved MCMC with active subspaces

Constantine et al. (2016) introduced a Metropolis-Hastings (MH) approach that target the active subspace of a posterior distribution: a linearly projected subspace that is informed by the likelihood.. Schuster et al. (2017) refined this approach to introduce a pseudo-marginal Metropolis-Hastings, integrating out inactive variables through estimating a marginal likelihood at every MH iteration. In this talk we show empirically that the effectiveness of these approaches is limited in the case where the linearity assumption is violated, and suggest a particle marginal Metropolis-Hastings algorithm as an alternative for this situation. The high computational cost of these approaches leads us to consider alternative approaches to using active subspaces in MCMC that avoid the need to estimate a marginal likelihood: we introduce Metropolis-within-Gibbs and Metropolis-within-particle Gibbs methods that provide a more computationally efficient use of the active subspace.

References:

• Improved MCMC with active subspaces, 2025

Joint work with Leonardo Ripoli (University of Reading)

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 #95

The ninety-fifth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, February 12, 2026.

2–3 PM — Yuansi Chen (ETH Zürich) — [slides]

When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?

We analyze the mixing time of Metropolized Hamiltonian Monte Carlo (HMC) with the leapfrog integrator to sample from a distribution on $\mathbb{R}^d$ whose log-density is smooth, has Lipschitz Hessian in Frobenius norm and satisfies isoperimetry. We bound the gradient complexity to reach $\epsilon$ error in total variation distance from a warm start by $O(d^{1/4} \polylog(1/\epsilon))$ and compare it to the minimax mixing rate of MALA. We discuss the benefit of the leapfrog integrator in HMC with short integration time.

References:

• Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Sampling, 2021
• When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?, 2023

Joint work with Khashayar Gatmiry (MIT) & Minhui Jiang (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.

UQSay #94

The ninety-fourth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, January 22 → February 05 (rescheduled), 2026.

2–3 PM — Eleni Chatzi (ETH Zürich, Department of Civil, Environmental and Geomatic Engineering) — [slides]

Dynamics, Inference, and Uncertainty: Foundations of AI-Enhanced Digital Twins

This talk examines the role of structural dynamics as a foundation for inference under uncertainty in AI-enhanced Digital Twins. Structural assets are highly individual, operate under variable environmental and operational conditions, and are only partially observable. In this context, dynamical signatures, extracted through structured inference schemes such as modal analysis, provide compact and physically interpretable representations through which uncertainty can be quantified, propagated, and reduced.

The talk discusses how physics-enhanced machine learning (PEML), together with structured representations and reduced-order models, enables potent yet efficient approximations that synergize with available data. By embedding physical constraints, governing equations, and dynamical structure into learning architectures, these models balance prior knowledge with data-driven adaptation, reducing epistemic uncertainty while remaining scalable under limited or evolving observations. Structured low-dimensional representations further support stable learning, efficient uncertainty propagation, and interpretable model updates.

By framing dynamics as the interface between physics and data within the context of inference, the talk highlights pathways toward uncertainty-aware, interpretable digital twins capable of supporting resilient decision-making of complex infrastructure systems.

References:

• Discussing the spectrum of physics-enhanced machine learning: a survey on structural mechanics applications, 2024 - github
• On the Consistent Classification and Treatment of Uncertainties in Structural Health Monitoring Applications, 2024
• Grammar-based Ordinary Differential Equation Discovery, 2025 - github
• Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamics, 2025 - github

Joint work with the further members of the group of Structural Mechanics & Monitoring at 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.