Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach

Bergel, Guy L.; Montes de Oca Zapiain, David; Romero, Vicente

doi:10.1017/dce.2023.17

Title: Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach

Journal Article · 22 October 2023 · Data-Centric Engineering

DOI: https://doi.org/10.1017/dce.2023.17 · OSTI ID:2329567

^[1];

^[2]; Romero, Vicente

Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

The finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrificing accuracy. However, these methods can produce biased predictions that deviate from those obtained with FEM, since these hybrid FEM-NN approaches rely on approximations trained using physically relevant quantities. In this work, an uncertainty estimation framework is introduced that leverages ensembles of Bayesian neural networks to produce diverse sets of predictions using a hybrid FEM-NN approach that approximates internal forces on a deforming solid body. The uncertainty estimator developed herein reliably infers upper bounds of bias/variance in the predictions for a wide range of interpolation and extrapolation cases using a three-element FEM-NN model of a bar undergoing plastic deformation. This proposed framework offers a powerful tool for assessing the reliability of physics-based surrogate models by establishing uncertainty estimates for predictions spanning a wide range of possible load cases.

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Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525

OSTI ID:: 2329567

Report Number(s):: SAND--2024-03657J

Journal Information:: Data-Centric Engineering, Journal Name: Data-Centric Engineering Journal Issue: 23 Vol. 4; ISSN 2632-6736

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach

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