Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids

Fuente: arXiv
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Auteurs principaux: Deshpande, Saurabh, Rappel, Hussein, Hobbs, Mark, Bordas, Stéphane P. A., Lengiewicz, Jakub
Format: Preprint
Publié: 2024
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author Deshpande, Saurabh
Rappel, Hussein
Hobbs, Mark
Bordas, Stéphane P. A.
Lengiewicz, Jakub
author_facet Deshpande, Saurabh
Rappel, Hussein
Hobbs, Mark
Bordas, Stéphane P. A.
Lengiewicz, Jakub
contents Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when input-output relationships are non-linear. To handle this problem, the present work introduces an innovative approach that combines autoencoder deep neural networks with the probabilistic regression capabilities of Gaussian processes. The autoencoder provides a low-dimensional representation of the solution space, while the Gaussian process is a Bayesian method that provides a probabilistic mapping between the low-dimensional inputs and outputs. We validate the proposed framework for its application to surrogate modeling of non-linear finite element simulations. Our findings highlight that the proposed framework is computationally efficient as well as accurate in predicting non-linear deformations of solid bodies subjected to external forces, all the while providing insightful uncertainty assessments.
format Preprint
id arxiv_https___arxiv_org_abs_2407_10732
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids
Deshpande, Saurabh
Rappel, Hussein
Hobbs, Mark
Bordas, Stéphane P. A.
Lengiewicz, Jakub
Computational Engineering, Finance, and Science
Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when input-output relationships are non-linear. To handle this problem, the present work introduces an innovative approach that combines autoencoder deep neural networks with the probabilistic regression capabilities of Gaussian processes. The autoencoder provides a low-dimensional representation of the solution space, while the Gaussian process is a Bayesian method that provides a probabilistic mapping between the low-dimensional inputs and outputs. We validate the proposed framework for its application to surrogate modeling of non-linear finite element simulations. Our findings highlight that the proposed framework is computationally efficient as well as accurate in predicting non-linear deformations of solid bodies subjected to external forces, all the while providing insightful uncertainty assessments.
title Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids
topic Computational Engineering, Finance, and Science
url https://arxiv.org/abs/2407.10732