Monday, June 28, 2021

UQSay #33

The thirty-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, July 1, 2021.

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.

Monday, June 14, 2021

UQSay #32

The thirty-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, June 17, 2021.

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.

Friday, May 28, 2021

UQSay #31

The thirty-first UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, June 3, 2021.

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.

Wednesday, May 12, 2021

UQSay #30

The thirtieth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, May 20, 2021.

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.

Monday, May 3, 2021

UQSay #29

The twenty-ninth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, May 6, 2021.

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.

Wednesday, April 14, 2021

UQSay #28

The twenty-eighth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, April 22, 2021.

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.

Saturday, March 27, 2021

UQSay #27

The twenty-seventh UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, April 1, 2021.

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.