Journal Article

Physics-informed neural networks for solving nonlinear diffusivity and Biot’s equations

Jørgensen, Thomas M., Kadeethum, Teeratorn, Nick, Hamidreza M.

2020

Overview

This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy harvesting. Specifically, we investigate how to extend the methodology of physics-informed neural networks to solve both the forward and inverse problems in relation to the nonlinear diffusivity and Biot's equations. We explore the accuracy of the physics-informed neural networks with different training example sizes and choices of hyperparameters. The impacts of the stochastic variations between various training realizations are also investigated. In the inverse case, we also study the effects of noisy measurements. Furthermore, we address the challenge of selecting the hyperparameters of the inverse model and illustrate how this challenge is linked to the hyperparameters selection performed for the forward one.

• Publisher: Public Library of Science,Public Library of Science (PLoS)
• Subject: Accuracy / Analysis / Applied mathematics / Artificial neural networks / Bias / Biology and Life Sciences / Biomedical engineering / Computer and Information Sciences / Computer science / Deep learning / Diffusivity / Earthquake prediction / Earthquakes / Electric power generation / Energy harvesting / Geophysical prediction / Hydrocarbons / Inverse problems / Mechanics / Neural networks / Neurons / Nonlinear theories / Partial differential equations / Permeability / Physical Sciences / Physics / Porous materials / Problems / Research and Analysis Methods / Seismic activity / Stochasticity / Thermal diffusivity / Training