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

• URL: http://arxiv.org/abs/2110.13680v1
• Date: Tue, 26 Oct 2021 13:18:06 GMT
• Title: Uncertainty quantification in a mechanical submodel driven by a Wasserstein-GAN
• Authors: Hamza Boukraichi, Nissrine Akkari, Fabien Casenave, David Ryckelynck
• Abstract summary: We show that the use of non-linear techniques in machine learning and data-driven methods is highly relevant. Generative Adversarial Networks (GANs) are suited for such applications, where the Wasserstein-GAN with gradient penalty variant offers improved results.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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