Bruno Sudret


Last Name

Sudret

First Name

Bruno

ORCID

0000-0002-9501-7395

Organisational unit

03962 - Sudret, Bruno / Sudret, Bruno

Search Results

Publications1 - 10 of 388
  • A new moment-independent measure for reliability-sensitivity analysis
    Item type: Other Conference Item
    Schmid, Florian; Marelli, Stefano; Sudret, Bruno (2019)
  • Bayesian stochastic polynomial chaos expansions for the approximation of stochastic simulators
    Item type: Other Conference Item
    Moustapha, Maliki; Sudret, Bruno (2025)
    Uncecomp 2025 Proceedings
    Stochastic simulators are increasingly popular in engineering and natural sciences, with applications spanning fields like wind energy, earthquake engineering, epidemiology, and mathematical finance, among others. Unlike deterministic simulators, which yield identical outputs when evaluated multiple times with the same input, stochastic simulators produce different outputs with each run. As a result, each output is a random variable, characterized by a conditional distribution or summary statistics, such as mean and variance. Accurately capturing these characteristics generally requires numerous model evaluations, particularly in uncertainty quantification where analyses are carried out for numerous inputs. To address the computational demand of these evaluations, stochastic emulators, which are efficient and inexpensive surrogate models for the simulators, have been developed. Examples include stochastic Kriging, generalized lambda models, and stochastic polynomial chaos expansions (SPCE) [1]. SPCE has proven especially effective, as it operates with minimal assumptions. For instance, unlike many other methods, it does not require specifying a particular distributional form for the conditional output distribution. In its original formulation, SPCE introduces a random latent variable to capture the intrinsic randomness of the simulator. A polynomial chaos expansions (PCE) model is then built in the joint input-latent space by sparse regression. The training process follows a two-step approach: first, the basis functions are selected using the mean output of the simulator, then the coefficients and the noise term's variance are jointly calibrated using maximum likelihood estimation. This process is conducted within a cross-validation scheme to get the best estimate of the noise variance. Overall, the entire procedure is computationally intensive and may sometimes result in a suboptimal model. Although effective in approximating complex stochastic simulators with limited data, this calibration approach has a few limitations. In this contribution, we propose a Bayesian framework to address the limitations in SPCE training. By defining a sparsity-inducing prior on the expansion coefficients, we provide a principled method for basis selection in the polynomial chaos expansions. Additionally, the prior on the noise variance acts as a regularizer, allowing us to bypass cross-validation while avoiding overfitting. We further explore various approaches for posterior estimation, including Hamiltonian Monte Carlo. Finally, we illustrate how this Bayesian setup enables us to quantify prediction uncertainty, which is particularly valuable in the context of active learning. References [1] Zhu, X. and B. Sudret (2023). Stochastic polynomial chaos expansions to emulate stochastic simulators. International Journal for Uncertainty Quantification 13 (2), 31-52.
  • Comparing probabilistic and p-box input modelling in structural reliability analysis
    Item type: Other Conference Item
    Schöbi, Roland; Sudret, Bruno (2016)
  • Dimensionality reduction and surrogate modelling for high-dimensional UQ problems
    Item type: Other Conference Item
    Lataniotis, Christos; Marelli, Stefano; Sudret, Bruno (2017)
  • Active learning methods for component- and system reliability analysis
    Item type: Other Conference Item
    Sudret, Bruno (2024)
    Structural reliability analysis evaluates the safety of structures and systems under uncertain conditions. Traditional simulation methods for estimating failure probability are computationally intensive. As an alternative, the past decade has seen the introduction of surrogate-based methods. These methods involve creating a metamodel of the original limit-state functions for use in reliability estimation algorithms. Active learning techniques iteratively refine the surrogate model's experimental design using suitable learning functions. This presentation surveys recent advancements in active learning for reliability analysis, identifying a common framework that includes a surrogate model, a reliability estimation algorithm, a learning function, and a stopping criterion. By non-intrusively integrating these components, we can reconstruct most existing active learning methods. We conducted a comprehensive benchmark of 39 active learning strategies across 20 selected reliability problems, resulting in approximately 12,000 analyses. This benchmarking helped identify performance patterns and generalization capabilities of different approaches, leading to best practice recommendations. The second part of the talk extends these methods to system reliability analysis, where surrogate models are developed for each limit state separately. We introduce an optimal enrichment scheme, informed by global sensitivity analysis, to prioritize surrogate model updates. The talk concludes with various structural engineering applications, showcasing the practical applications of these methods
  • Calcul des courbes de fragilité sismique par approches non-paramétriques
    Item type: Conference Paper
    Sudret, Bruno; Mai, C.V. (2013)
    Congrès français de mécanique 2013 : du 26 au 30 août 2013 Bordeaux
  • Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models
    Item type: Other Conference Item
    Zhu, Xujia; Sudret, Bruno (2019)
    Global sensitivity analysis aims at quantifying the impact of input variables (taken separately or as a group) onto the variation of the response of a computational model. Classically, such models (also called simulators) are deterministic, in the sense that repeated runs provide the same output quantity of interest. In contrast, stochastic simulators return different results when run twice with the same input values due to additional sources of stochasticity in the code itself. In other words, the output of a stochastic simulator is a random variable for a given vector of input parameters. Many sensitivity measures, such as the Sobol’ indices and Borgonovo indices [1], have been developed in the context of deterministic simulators. They can be directly extended to stochastic simulators [2,3], despite the additional randomness of the latter. The calculation of such measures can be carried out through Monte Carlo simulation, which would require many model evaluations though. However, high-fidelity models are often time-consuming: a single model run may require hours or even days. In consequence, direct application of Monte Carlo simulations to calculate sensitivity measures becomes intractable. To alleviate the computational burden, surrogate models are constructed so as to mimic the original numerical model at a smaller computational cost though. For deterministic simulators, surrogate models have been successfully developed over the last decade, e.g. polynomial chaos expansions [4]. However, the question of appropriate surrogate modelling for stochastic simulators arose only recently in engineering. In this study, we propose to use generalized lambda distributions to flexibly approximate the response of a stochastic simulator. Under this setting, the parameters of the generalized lambda distribution become deterministic functions of the input variables. In this contribution we use sparse polynomial chaos expansions to represent the latter. To construct such a sparse generalized lambda model, we develop an algorithm that combines feasible generalized least-squares with stepwise regression. This method does not require repeated model evaluations for the same input parameters to account for the random nature of the output, and thus it reduces the total number of model runs drastically. Once the stochastic emulator is constructed, one can easily evaluate the conditional mean and variance, which is needed for the Sobol’ indices calculation. Because the generalized lambda distribution parametrizes the output quantile function, the surrogate model is expressed as a deterministic function of the input variables and a latent uniform random variable that represents the randomness of the output. As a result, instead of calculating the Sobol’ indices for each input variable through sampling, we can derive analytically the Sobol’ indices by some suitable post-processing. Moreover, the generalized lambda model provides the conditional distribution of the output given any input parameters. Therefore, distribution-based sensitivity measures, such as Borgonovo indices, can also be calculated straightforwardly. [1] E. Borgonovo, A new uncertainty importance measure. Reliab. Eng. Sys. Safety, 92:771-784, 2007. [2] A. Marrel, B. Iooss, S. Da Veiga, and M. Ribatet, Global sensitivity analysis of stochastic computer models with joint metamodels, Stat. Comput., 22:833-847, 2012. [3] M. N. Jimenez, O. P. Le Maître, and O. M. Knio, Nonintrusive polynomial chaos expansions for sensitivity analysis in stochastic differential equations, 5:378-402, 2017 [4] B. Sudret, Global sensitivity analysis using polynomial chaos expansions, Reliab. Eng. Sys. Safety, 93:964-979, 2008
  • Uncertainty quantification using surrogate modelling
    Item type: Other Conference Item
    Sudret, Bruno (2023)
    Nowadays, computational models have become an integral part of various fields of applied sciences and engineering. These models are used to forecast the behaviour of complex natural or man-made systems. Also known as simulators, they enable engineers and scientists to evaluate a system's performance in a virtual environment, and then help optimize its design or operation. Simulators, such as high-fidelity finite element models, often comprise numerous parameters, and their execution is expensive, even when using the available computing power to the fullest. Additionally, the complexity of a system leads to greater uncertainty in its governing parameters, environmental and operating conditions. In this context, uncertainty quantification (UQ) methods have gained popularity in both academia and industry in recent times, as they can be used to address reliability, sensitivity, or optimal design problems. Monte Carlo simulation, a well-known brute-force method, uses random number generation to solve these questions. However, it may require thousands to millions of simulations to produce accurate predictions, making it impractical for high-fidelity simulators. In contrast, surrogate models can solve these UQ problems by creating an accurate approximation of the simulator’s response, using a limited number of runs at selected values (the experimental design) and a learning algorithm. In this lecture, we will first introduce the general features of surrogate models and their relationship with machine learning. Next, we will discuss polynomial chaos expansions in detail, along with their sparse version for high-dimensional problems. We will also address recent extensions to structural dynamics.
  • On constrained distribution-free p-boxes and their propagation
    Item type: Conference Paper
    Daub, Marco; Marelli, Stefano; Sudret, Bruno (2021)
    Proceedings of the 9th International Workshop on Reliable Engineering Computing (REC 2021)
    Propagating uncertainties through computational models is a key ingredient in uncertainty quantification in engineering. In general, uncertainty can be characterized as aleatoric, caused by variability, and epistemic, caused by lack of knowledge. Imprecise probability theory offers a natural framework to deal with both through, through sets of probability distributions. Among the latter, probability-boxes (p-boxes), which specify upper and lower bounds on admissible cumulative distribution functions (CDFs), are well established in the literature. We hereby introduce a novel class of p-boxes, constrained distribution-free p-boxes, that is based on imposing constraints on the admissible distributions (e.g. bound moments, symmetry, derivatives, etc.) on otherwise distribution-free p-boxes. We demonstrate that this class maintains most of the flexibility of classical distribution-free p-boxes, while avoiding most of the non-physical configurations it can be associated with. We also show how constrained distribution-free p-boxes can influence uncertainty bounds in the model predictions, thus improving the quality of the resulting uncertainty estimation.
  • A global framework for active learning reliability in UQLab
    Item type: Other Conference Item
    Moustapha, Maliki; Marelli, Stefano; Sudret, Bruno (2022)
Publications1 - 10 of 388