We propose a novel approach to model viscoelasticity materials using neural networks, which capture rate-dependent and nonlinear constitutive relations. However, 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 multi-physics interactions. We show that limited displacement data hold 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 physics constrained learning. The effectiveness of our method is demonstrated through numerous benchmark problems in geomechanics and porous media transport.
Inverse Modeling of Viscoelasticity Materials using Physics Constrained Learning
Kailai Xu,A. Tartakovsky,J. Burghardt,Eric F Darve
Published 2020 in arXiv.org
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- Publication year
2020
- Venue
arXiv.org
- Publication date
2020-05-09
- Fields of study
Materials Science, Physics, Computer Science, Mathematics, Engineering
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