Inverse Estimation of Elastic Modulus Using Physics-Informed Generative Adversarial Networks

• URL: http://arxiv.org/abs/2006.05791v1
• Date: Wed, 20 May 2020 20:14:10 GMT
• Title: Inverse Estimation of Elastic Modulus Using Physics-Informed Generative Adversarial Networks
• Authors: James E. Warner, Julian Cuevas, Geoffrey F. Bomarito, Patrick E. Leser, William P. Leser
• Abstract summary: Agenerative adversarial networks (GANs) encode physical laws in the form of partial differential equations (PDEs) In this work, PI-GANs are demonstrated for the application of elastic modulus estimation in mechanical testing. Two feed-forward deep neural network generators used to model the deformation and material stiffness across a two dimensional domain.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While standard generative adversarial networks (GANs) rely solely on training data to learn unknown probability distributions, physics-informed GANs (PI-GANs) encode physical laws in the form of stochastic partial differential equations (PDEs) using auto differentiation. By relating observed data to unobserved quantities of interest through PDEs, PI-GANs allow for the estimation of underlying probability distributions without their direct measurement (i.e. inverse problems). The scalable nature of GANs allows high-dimensional, spatially-dependent probability distributions (i.e., random fields) to be inferred, while incorporating prior information through PDEs allows the training datasets to be relatively small. In this work, PI-GANs are demonstrated for the application of elastic modulus estimation in mechanical testing. Given measured deformation data, the underlying probability distribution of spatially-varying elastic modulus (stiffness) is learned. Two feed-forward deep neural network generators are used to model the deformation and material stiffness across a two dimensional domain. Wasserstein GANs with gradient penalty are employed for enhanced stability. In the absence of explicit training data, it is demonstrated that the PI-GAN learns to generate realistic, physically-admissible realizations of material stiffness by incorporating the PDE that relates it to the measured deformation. It is shown that the statistics (mean, standard deviation, point-wise distributions, correlation length) of these generated stiffness samples have good agreement with the true distribution.

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