Thursday, January 30, 2020

UQSay #08

The eighth UQSay seminar on Uncertainty Quantification and related topics, organized by L2S, Anses, MSSMAT, and EDF R&D will take place on Thursday afternoon, February 27, 2020, at CentraleSupelec Paris-Saclay (Eiffel building, amphi V).

(Please fill this: Evento if you intend to come.)
14h — David Makowski (INRAE)

The role of uncertainty analysis in biological invasion risk analysis

Biological invasions have sometimes spectacular consequences on our environment. They can have impacts on agricultural production, on human health and sometimes even call into question the existence of certain economic sectors. In order to assess the risks of potentially harmful organisms and identify appropriate management measures, numerous risk analyses are carried out every year by scientists from various disciplines in different countries. However, the likelihood of entry, establishment, spread of a biological organism and its potential impact depend on many uncertain factors. In this presentation, I will describe the main approaches used to conduct uncertainty analyses in this area and discuss their relevance and limitations for decision support.

15h — Myriam Merad (UMR LAMSADE, PSL*, CNRS, Univ. Paris Dauphine)

Considerations around the concepts of uncertainty, risk and decision making in safety, security, environment and health

Through several operational examples, we will discuss the links between risks, uncertainties and decisions and the effect of modeling processes on decision support.

References: see ResearchGate and the book "Expertise Under Scrutiny".

Organizers: Emmanuel Vazquez (L2S), Laurent Guillier (Anses) and Julien Bect (L2S).

Saturday, December 14, 2019

UQSay #07

The seventh UQSay seminar on Uncertainty Quantification and related topics, organized by L2S and MSSMAT, will take place on Thursday afternoon, January 16, 2020, at CentraleSupelec Paris-Saclay (Eiffel building, amphi III).

We will have two talks:

14h — Bertrand Iooss (EDF R&D / PRISME dept.) — [slides]

Iterative estimation in uncertainty and sensitivity analysis

While building and using numerical simulation models, uncertainty and sensitivity analysis are invaluable tools. In engineering studies, numerical model users and modellers have shown high interest in these techniques that require to run many times the simulation model with different values of the model inputs in order to compute statistical quantities of interest (QoI, i.e. mean, variance, quantiles, sensitivity indices…). In this talk we will focus on new issues relative to large scale numerical systems that simulate complex spatial and temporal evolutions. Indeed, the current practice consists in the storage of all the simulation results. Such a storage becoming quickly overwhelming, with the associated long read time that makes cpu time consuming the estimation of the QoI. One solution consists in avoiding this storage and in computing QoI on the fly (also called in-situ). It turns the problem to considering problems of iterative statistical estimation. The general mathematical and computational issues will be posed, and a particular attention will be paid to the estimation of quantiles (via an adaptation of the Robbins-Monro algorithm) and variance-based sensitivity indices (the so-called Sobol' indices).

Joint work with Yvan Fournier (EDF), Bruno Raffin (INRIA), Alejandro Ribés (EDF), Théophile Terraz (INRIA).

Refs: hal-01607479 and hal-02016828.

Related software: Melissa.

15h — Bruno Barracosa (EDF R&D / EFESE dept. and L2S) — [slides1 + slides2]

Bayesian Multi-objective Optimization with Noisy Evaluations using the Knowledge Gradient

We consider the problem of multi-objective optimization in the case where each objective is a stochastic black box that provides noisy evaluation results. More precisely, let f_1, ..., f_q be q real-valued objective functions defined on a search domain 𝕏 ⊂ ℝ^d, and assume that, for each x ∈ 𝕏, we can observe a noisy version of the objectives: Z_1 = f_1(x) + ε_1, ..., Z_q = f_q(x) + ε_q, where the ε_i's are zero-mean random variables. Our objective is to estimate the Pareto-optimal solutions of the problem: min f_1, ..., f_q.

We adopt a Bayesian optimization approach, which is a classical approach when the affordable number of evaluations is severely limited. In essence, Bayesian optimization consists in choosing a probabilistic model for the outputs Z_i and defining a sampling criterion to select evaluation points in the search domain 𝕏. Here, we propose to discuss the extension of the Knowledge Gradient approach of Frazier, Powell and Dayanik (INFORMS J. Comput., 21(4):599–613, 2009) to multi-objective problems with noisy evaluations. For instance, such an extension has been recently proposed by Astudillo and Frazier.

Joint work with Julien Bect (L2S), Héloïse Baraffe (EDF), Juliette Morin (EDF), Gilles Malarange (EDF) and Emmanuel Vazquez (L2S).

Organizers: Julien Bect (L2S) and Fernando Lopez Caballero (MSSMAT).

Tuesday, November 12, 2019

UQSay #06

The sixth UQSay seminar on Uncertainty Quantification and related topics, organized by L2S and MSSMAT, will take place on Thursday afternoon, November 28, 2019, at CentraleSupelec Paris-Saclay (Eiffel building, amphi V).

We will have two talks:

14h — Zhiguo Zeng (LGI) — [slides]

Remaining useful life prediction with imprecise and partial information:
An evidential hidden Markov model-based approach

Industrial systems often degrade before failure occurs. True degradation states, however, are often hidden and cannot be observed directly. Condition-monitoring data, e.g., noise, vibration, on the other hand, are available from sensors and contain information on the degradation process. Apart from condition-monitoring data, sometimes inspections can be made to directly observe the system degradation state. The inspection data, however, are often imprecise and contain only partial information on the true degradation states.

In this talk, we present an evidential hidden Markov model-based approach to integrate condition-monitoring data with inspection data for degradation state estimation and remaining useful life prediction. The degradation process is modeled by a discrete state continuous time Markov chain. The condition-monitoring data are modeled by a Gaussian mixture model given the true degradation state. Inspection data are modeled using evidence theory. Condition-monitoring data and inspection data are integrated in the framework of evidence theory and the parameters in the degradation model are estimated through expectation maximization algorithm. Remaining useful life of the system is, then, predicted based on the estimated parameters. The developed methods are tested through some numerical experiments and applied on a real case study of bearing degradation data from literature.

Joint work with Tangfan Xiahou and Yu Liu.

15h — Zicheng Liu (Chaire C2M) — [slides]

Surrogate modeling based on resampled polynomial chaos expansions

In surrogate modeling, polynomial chaos expansion (PCE) is popularly utilized to represent the random model responses. Recently, efforts have been made on improving the prediction performance of the PCE-based model and building efficiency by only selecting the influential basis polynomials (e.g., via the approach of least angle regression). An approach, named as resampled PCE (rPCE), is proposed to further optimize the selection by making use of the knowledge that the true model is fixed despite the statistical uncertainty inherent to sampling in the training. By simulating data variation via resampling (k-fold division utilized here) and collecting the selected polynomials with respect to all resamples, polynomials are ranked mainly according to the selection frequency. The resampling scheme (the value of k here) matters much and various configurations are considered and compared. The proposed resampled PCE is implemented with two popular selection techniques, namely least angle regression and orthogonal matching pursuit, and a combination thereof. The performance of the proposed algorithm is demonstrated on two analytical examples, a benchmark problem in structural mechanics, as well as a realistic case study in computational dosimetry.

Joint work with Dominique Lesselier, Bruno Sudret and Joe Wiart.

Reference: hal-01889651.

Organizers: Julien Bect (L2S), Fernando Lopez Caballero (MSSMAT) and Emmanuel Vazquez (L2S).

No registration is needed, but a simple email would be appreciated if you intend to come.

Friday, October 18, 2019

UQSay #05

The fifth UQSay seminar, organized by L2S and MSSMAT, will take place on Thursday afternoon, October 31, 2019, at CentraleSupelec Paris-Saclay (Eiffel building, amphi IV).

We will have two talks:

14h — Gildas Mazo (INRA) — [slides]

A tradeoff between explorations and repetitions in global sensitivity analysis for stochastic computer models

Global sensitivity analysis often accompanies computer modeling to understand what are the important factors of a model of interest. In particular, Sobol indices, naturally estimated by Monte-Carlo methods, permit to quantify the contribution of the inputs to the variability of the output. However, stochastic computer models raise difficulties. There is no unique definition of Sobol indices and their estimation is difficult because a good balance between repetitions of the computer code and explorations of the input space must be found. The problem of finding an optimal tradeoff between explorations and repetitions is addressed. Two Sobol indices are considered, their estimators constructed and their asymptotic properties established. To find an optimal tradeoff between repetitions and explorations, a tractable error criterion, which is small when the inputs of the model are ranked correctly, is built and minimized under a fixed computing budget. Then, Sobol estimates based on the balance found beforehand are produced. Convergence rates are given and it is shown that this method is asymptotically oracle. Numerical tests and a sensitivity analysis of a Susceptible-Infectious-Recovered (SIR) model are performed.

Reference: hal-02113448.

15h — Emmanuel Gobet (CMAP) — [slides]

Meta-model of a large credit risk portfolio in the Gaussian copula model

We design a meta-model for the loss distribution of a large credit portfolio in the Gaussian copula model. Using both the Wiener chaos expansion on the systemic economic factor and a Gaussian approximation on the associated truncated loss, we significantly reduce the computational time needed for sampling the loss and therefore estimating risk measures on the loss distribution. The accuracy of our method is confirmed by many numerical examples.

Joint work with Florian Bourgey and Clément Rey.

Reference: hal-02291548v2.

Organizers: Julien Bect (L2S) and Fernando Lopez Caballero (MSSMAT).

No registration is needed, but an email would be appreciated if you intend to come.

Monday, September 9, 2019

UQSay #04

The fourth UQSay seminar, organized by L2S and MSSMAT, will take place on Thursday afternoon, October 3, 2019, at CentraleSupelec Paris-Saclay (Eiffel building, amphi V).

We will have two talks:

14h — Merlin Keller (EDF R&D / PRISME dept.) — [slides]

Bayesian calibration and validation of a numerical model: an overview

Computer experiments are widely used in industrial studies to complement or replace costly physical experiments, in many applications: design, reliability, risk assessment, etc. One main concern with such a widespread use is the confidence one can have in the outcome of a numerical simulation, that aims to mimick an actual physical phenomenon. Indeed, the result of a simulation is tainted by different sources of uncertainty: numerical, parametric, due to modelisation and/or extrapolation, to cite only a few. Quantifying all sources of uncertainty, and their influence on the result of the study, is the primary goal of the verification, validation and uncertainty quantification (VVUQ) framework. An important step of VVUQ is calibration, wherein uncertain parameters within the computer model are tuned to reduce the gap between computations and available field measures.
   EDF R&D has devoted considerable efforts in the last few years to develop generic, mathematically well-grounded and computationally efficient calibration and validation methods, adapted to industrial applications. Two PhD programs and a post-doc have been devoted to this subject, whose main outcomes are reviewed in this talk. Hence, we will present the main methods available today to quantify and reduce the uncertainty on the result of a numerical experiment through calibration (from ordinary least squares (OLS) to sequential strategies adapted to costly black-box models) and validation, seen as the task of detecting and accounting for a possible systematic model bias (or model discrepancy) term, based on Bayesian model averaging. All proposed methods are illustrated using several industrial case studies, and we discuss available implementations.

Joint work with Pierre Barbillon, Mathieu Carmassi, Matthieu Chiodetti, Guillaume Damblin, Cédric Gœury, Kaniav Kamary, Éric Parent.

References: arXiv:1711.10016, arXiv:1903.03387, arXiv:1801.01810, arXiv:1808.01932.

15h — Didier Clouteau (MSSMAT) — [slides]

Blending Physics-Based numerical simulations and seismic databases using Generative Adversarial Network (GAN)

On the one hand, High Performance Computing (HPC) allows the numerical simulation of highly complicated physics-based scenarios accounting, to a certain extent, for Uncertainty Quantification and Propagation (UQ). On the second hand, Machine Learning (ML) techniques and Artificial Neural Networks (ANN) have reached outstanding but yet-not-fully-understood prediction capabilities for both supervised and unsupervised learning, at least in fields such as image or speech recognition. Yet, ANN are both prone to overfitting and highly sensitive to outliers questioning their usefulness in risk assessment studies. However, development of generative networks has allowed to better constrain the ANN responses and quantify the related Uncertainty. Adversarial training techniques have also appeared to provide a generic and efficient way to train these generative networks on huge un-labelled datasets.
   In this talk, we will first show how Generative Adversarial Networks (GAN) can be cast and used in the framework of Uncertainty quantification. Then we will propose an adversarial Generative Auto-Encoder aiming at transforming medium resolution signals obtained by physics-based methods into broadband seismic signals similar to those recorded in seismic databases.

Joint work with Filippo Gatti.

References: DOI:10.1785/0120170293 and hal-01860115.

Organizers: Julien Bect (L2S) and Fernando Lopez Caballero (MSSMAT).

No registration is needed, but an email would be appreciated if you intend to come.

Wednesday, May 8, 2019

UQSay #03

The third UQSay seminar, organized by L2S and EDF R&D, will take place on Thursday afternoon, June 13, 2019, at CentraleSupelec Paris-Saclay (Eiffel building, amphi V).

We will have two talks:

14h — Alexandre Janon (Laboratoire de Mathématique d'Orsay) — [slides]

Consistency of Sobol indices with respect to stochastic ordering of input parameters — Global optimization using Sobol indices

In the past decade, Sobol’s variance decomposition have been used as a tool - among others - in risk management. We show some links between global sensitivity analysis and stochastic ordering theories. This gives an argument in favor of using Sobol’s indices in uncertainty quantification, as one indicator among others.

Reference: (hal-01026373)

We propose and assess a new global (derivative-free) optimization algorithm, inspired by the LIPO algorithm, which uses variance-based sensitivity analysis (Sobol indices) to reduce the number of calls to the objective function. This method should be efficient to optimize costly functions satisfying the sparsity-of-effects principle.

Reference: hal-02154121
15h — Pierre Barbillon (MIA Paris) — [slides]

Sensitivity analysis of spatio-temporal models describing nitrogen transfers, transformations and losses at the landscape scale

Modelling complex systems such as agroecosystems often requires the quantification of a large number of input factors. Sensitivity analyses are useful to determine the appropriate spatial and temporal resolution of models and to reduce the number of factors to be measured or estimated accurately. Comprehensive spatial and temporal sensitivity analyses were applied to the NitroScape model, a deterministic spatially distributed model describing nitrogen transfers and transformations in rural landscapes. Simulations were led on a theoretical landscape that represented five years of intensive farm management and covering an area of 3km2. Cluster analyses were applied to summarize the results of the sensitivity analysis on the ensemble of model outputs.The methodology we applied is useful to synthesize sensitivity analyses of models with multiple space-time input and output variables and could be ported to other models than NitroScape.

Reference: (arXiv:1709.08608)

Organizers: Julien Bect (L2S) and Bertrand Iooss (EDF R&D).

No registration is needed, but an email would be appreciated if you intend to come.

Thursday, March 28, 2019

UQSay #02

The second UQSay seminar, organized by L2S and MSSMAT, will take place on Thursday afternoon, April 18, 2019, at CentraleSupelec Paris-Saclay (Eiffel building, amphi V, next to the one where we had UQSay #01).

We will have two talks, and hopefully some coffee in between:

14h — Chu Mai (EDF R&D / MMC dept) — [slides]

Prediction of crack propagation kinetics through
multipoint stochastic simulations of microscopic fields

Prediction of crack propagation kinetics in the components of nuclear plant primary circuits undergoing Stress Corrosion Cracking (SCC) can be improved by a refinement of the SCC models. One of the steps in the estimation of the time to rupture is the crack propagation criterion. Current models make use of macroscopic measures (e.g. stress, strain,..) obtained for instance using the Finite Element Method. To go down to the microscopic scale and use local measures, a two steps approach is proposed. First, synthetic microstructures representing the material under specific loadings are simulated, and their quality is validated using statistical measures. Second, the shortest path to rupture in terms of propagation time is computed, and the distribution of those synthetic times to rupture is compared with the time to rupture estimated only from macroscopic values. The first step is realized with the Cross Correlation Simulation (CCSIM), a multipoint simulation algorithm that produces synthetic stochastic fields from a training field. The Earth Mover's Distance is the metric which allows to assess the quality of the realizations. The computation of shortest paths is realized using Dijkstra's algorithm. This approach allows to obtain a refinement in the prediction of the kinetics of crack propagation compared to the macroscopic approach. An influence of the loading conditions on the distribution of the computed synthetic times to rupture was observed, which could be reduced through a more robust use of the CCSIM.

Ref: hal-02068315

15h — Olivier Le Maître (LIMSI) — [slides]

Surrogate models and reduction methods for UQ
and inference in large-scale models

Uncertainty Quantification (UQ) and Global Sensitivity Analysis (GSA) in numerical models often rely on sampling approaches (either random or deterministic) that call for many resolutions of the model. Even though these computations can usually be carried out in parallel, the application of UQ and GSA methods to large-scale simulations remains challenging, both from the computational, storage and memory points of view. Similarly, Bayesian inference and assimilation problems can be favorably impacted by over-abundant observations, because of over-constrained update problems or numerical issues (overflows, complexity,...), raising the question of observations reduction.
A solution to alleviate the computational burden is to use a surrogate model of the full large scale model, that can be sampled extensively to estimate sensitivity coefficients and characterize the prediction uncertainty. However, building a surrogate for the whole large scale model solution can be extremely demanding and reduction strategies are needed. In this talk, I will introduce several techniques for the reduction of the model output and the construction of its surrogate. Some of these techniques will be illustrated on ocean circulation model simulations. For the reduction of observations, I will discuss and compare few strategies based on information theoretical considerations that have been recently proposed for the Bayesian framework.

Refs: [1], [2], [3], [4], [5], [6].


  • Julien Bect (L2S),
  • Fernando Lopez Caballero (MSSMAT),
  • and Didier Clouteau (MSSMAT).

No registration is needed, but an email would be appreciated if you intend to come.