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Journal of Machine Learning for Modeling and Computing

ISSN Imprimir: 2689-3967
ISSN On-line: 2689-3975

Journal of Machine Learning for Modeling and Computing

DOI: 10.1615/.2020033325
pages 1-17


Ari L. Frankel
Sandia National Laboratories, Livermore, California, 94551, USA
Reese E. Jones
Sandia National Laboratories, Livermore, California, 94551, USA
Laura P. Swiler
Optimization and Uncertainty Quantification Department, Sandia National Laboratories, P.O. Box 5800, MS 1318, Albuquerque, New Mexico 87185, USA


In this work, we develop Gaussian process regression (GPR) models of isotropic hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this approach that embeds rotational invariance of the stress-stretch constitutive relation in the GPR representation. This approach requires fewer training examples and achieves higher accuracy while maintaining invariance to rotations exactly. Finally, we consider an approach that recovers the strain-energy density function and derives the stress tensor from this potential. Although the error of this model for predicting the stress tensor is higher, the strain-energy density is recovered with high accuracy from limited training data. The approaches presented here are examples of physics-informed machine learning. They go beyond purely data-driven approaches by embedding the physical system constraints directly into the Gaussian process representation of materials models.


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