Uncertainty quantification in a mechanical submodel driven by a Wasserstein-GAN

TL;DR

This paper presents a novel approach using Wasserstein-GANs to generate stochastic boundary conditions for fast finite element simulations, enabling efficient uncertainty quantification in large dynamical systems with complex uncertainties.

Contribution

It introduces a data-driven method employing Wasserstein-GANs with gradient penalty to learn probabilistic boundary conditions for non-parametric uncertainties in mechanical submodels.

Findings

Wasserstein-GANs improve convergence in stochastic boundary condition generation.

The method enables fast Monte Carlo simulations for uncertainty quantification.

Application demonstrated on finite element models with promising results.

Abstract

The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis can be used when systems undergo low-frequency vibrations. In the case of fast dynamics and wave propagation, we investigate a random generator of boundary conditions for fast submodels by using machine learning. We show that the use of non-linear techniques in machine learning and data-driven methods is highly relevant. Physics-informed neural networks is a possible choice for a data-driven method to replace linear modal analysis. An architecture that support a random component is necessary for the construction of the stochastic model of the physical system for non-parametric uncertainties, since the goal is to learn the underlying probabilistic distribution of uncertainty in the data. Generative Adversarial Networks (GANs) are suited for such applications, where the Wasserstein-GAN with gradient penalty variant offers improved convergence results for our problem. The objective of our approach is to train a GAN on data from a finite element method code (Fenics) so as to extract stochastic boundary conditions for faster finite element predictions on a submodel. The submodel and the training data have both the same geometrical support. It is a zone of interest for uncertainty quantification and relevant to engineering purposes. In the exploitation phase, the framework can be viewed as a randomized and parametrized simulation generator on the submodel, which can be used as a Monte Carlo estimator.