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)


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.

Monday, March 15, 2021

UQSay #26

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

2–3 PM — Amaya Nogales Gómez (I3S, Sophia Antipolis) — [slides]


Incremental space-filling design based on coverings and spacings: improving upon low discrepancy sequences

The paper addresses the problem of defining families of ordered sequences {x_i} i∈N of elements of a compact subset X of R^d whose prefixes X_n = {x_i} i=1, ..., n, for all orders n, have good space-filling properties as measured by the dispersion (covering radius) criterion. Our ultimate aim is the definition of incremental algorithms that generate sequences X_n with small optimality gap, i.e., with a small increase in the maximum distance between points of X and the elements of X_n with respect to the optimal solution X_n. The paper is a first step in this direction, presenting incremental design algorithms with proven optimality bound with respect to one-parameter families of criteria based on coverings and spacings that both converge to dispersion for large values of their parameter.

Joint work with Luc Pronzato and Maria-Joao Rendas.

Ref: hal-02987983.

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, March 1, 2021

UQSay #25

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

2–3 PM — Victor Picheny (Secondmind) — [slides]


Bayesian optimisation: ablation study, global performance assessment and improvements based on trust regions

Bayesian Optimisation algorithms (BO) are global optimisation methods that iterate by constructing and using conditional Gaussian processes (GP). It is a common claim that BO is state-of-the-art for costly functions. However, this claim is weakly supported by experimental evidence, as BO is most often compared to itself, rather than to algorithms of different nature.

In this work, we study the performance of BO within the well-known COmparing Continuous Optimizers benchmark (COCO). We first analyse the sensitivity of BO to its own parameters, enabling us to answer general questions regarding the choice of the GP kernel or its trend, the initial GP budget, and the suboptimisation of the acquisition function. Then, we study on which function class and dimension BO is relevant when compared to state-of-the-art optimisers for expensive functions.

The second part of this talk describes a new BO algorithm to improve scalability with dimension, called TREGO (trust-region-like efficient global optimisation). TREGO alternates between regular BO steps and local steps within a trust region. By following a classical scheme for the trust region (based on a sufficient decrease condition), we demonstrate that our algorithm enjoys strong global convergence properties, while departing from EGO only for a subset of optimization steps. The COCO benchmark experiments reveal that TREGO consistently outperforms EGO and closes the performance gap with other state-of-the-art algorithms in conditions (high budget and dimension) for which BO was struggling to compete previously.

Joint work Youssef Diouane, Rodolphe Le Riche, Alexandre Scotto Di Perrotolo.

Ref: arXiv:2101.06808 & DiceOptim.

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.

Tuesday, February 9, 2021

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) — [slides]


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 ICSREAM 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.

Wednesday, January 27, 2021

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) — [slides]


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).

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.