Learning viscoelasticity models from indirect data using deep neural networks

Xu, Kailai; Tartakovsky, Alexandre M.; Burghardt, Jeff; Darve, Eric

doi:10.1016/j.cma.2021.114124

Title: Learning viscoelasticity models from indirect data using deep neural networks

Journal Article · 15 December 2021 · Computer Methods in Applied Mechanics and Engineering

DOI: https://doi.org/10.1016/j.cma.2021.114124 · OSTI ID:1827254

^[1]; Tartakovsky, Alexandre M. ^[2];

^[2];

^[1]

Stanford Univ., CA (United States)
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

In this study, we propose a novel approach to model viscoelasticity materials, where rate-dependent and non-linear constitutive relationships are approximated with deep neural networks. We assume that inputs and outputs of the neural networks are not directly observable, and therefore common training techniques with input–output pairs for the neural networks are inapplicable. To that end, we develop a novel computational approach to both calibrate parametric and learn neural-network-based constitutive relations of viscoelasticity materials from indirect displacement data in the context of multiple-physics systems. We show that limited displacement data holds sufficient information to quantify the viscoelasticity behavior. We formulate the inverse computation – modeling viscoelasticity properties from observed displacement data – as a PDE-constrained optimization problem and minimize the error functional using a gradient-based optimization method. The gradients are computed by a combination of automatic differentiation and implicit function differentiation rules. The effectiveness of our method is demonstrated through numerous benchmark problems in geomechanics and porous media transport.

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Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Stanford University, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC05-76RL01830; SC0019205; SC0019453

OSTI ID:: 1827254

Report Number(s):: PNNL-SA--154901

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 387; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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