Learning viscoelasticity models from indirect data using deep neural networks

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

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Article number114124
JournalComputer Methods in Applied Mechanics and Engineering
Volume387
DOIs
StatePublished - Dec 15 2021
Externally publishedYes

Keywords

  • Deep learning
  • Geomechanics and multi-phase flow
  • Neural networks
  • Viscoelasticity

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications

Fingerprint

Dive into the research topics of 'Learning viscoelasticity models from indirect data using deep neural networks'. Together they form a unique fingerprint.

Cite this