Physics-informed Neural Networks for Solving Nonlinear Diffusivity and Biot's equations
This work addresses multiphysics problems relevant to biomedical engineering, earthquake prediction, and underground energy harvesting, but it is incremental as it extends an existing method to new equations.
The paper tackled solving nonlinear multiphysics problems, such as nonlinear diffusivity and Biot's equations, using physics-informed neural networks for both forward and inverse cases, achieving results that depend on training sizes, hyperparameters, and noise levels, though no concrete numbers are provided.
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.