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

TL;DR

This paper introduces a novel surrogate modeling framework combining autoencoder neural networks with Gaussian process regression to efficiently and accurately predict nonlinear solid mechanics behaviors while quantifying uncertainty.

Contribution

The work presents an innovative integration of autoencoders with Gaussian processes for probabilistic surrogate modeling in nonlinear mechanics, addressing high-dimensional uncertainty quantification.

Findings

Framework is computationally efficient.

Accurately predicts nonlinear deformations.

Provides reliable uncertainty estimates.

Abstract

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.