# Physics-informed Neural Networks for Solving Nonlinear Diffusivity and Biot's equations

arXiv: https://arxiv.org/abs/2002.08235 · HTML: https://mlsanity.com/paper/2002.08235/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2020.

## Built on by (most cited first, 20 of 20)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
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- [Interval and fuzzy physics-informed neural networks for uncertain fields](https://mlsanity.com/paper/2106.13727/) (2021)
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- [Physics-informed neural network solution of thermo-hydro-mechanical (THM) processes in porous media](https://mlsanity.com/paper/2203.01514/) (2022)
- [Non-intrusive reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation](https://mlsanity.com/paper/2101.11810/) (2021)
- [Physics-informed attention-based neural network for solving non-linear partial differential equations](https://mlsanity.com/paper/2105.07898/) (2021)
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- [Inverse modeling of nonisothermal multiphase poromechanics using physics-informed neural networks](https://mlsanity.com/paper/2209.03276/) (2022)
- [Temporal Consistency Loss for Physics-Informed Neural Networks](https://mlsanity.com/paper/2301.13262/) (2023)
- [Physics-Informed DeepONet Coupled with FEM for Convective Transport in Porous Media with Sharp Gaussian Sources](https://mlsanity.com/paper/2508.19847/) (2025)
- [Learning Generic Solutions for Multiphase Transport in Porous Media via the Flux Functions Operator](https://mlsanity.com/paper/2307.01354/) (2023)
- [Efficient machine-learning surrogates for large-scale geological carbon and energy storage](https://mlsanity.com/paper/2310.07461/) (2023)
- [A Physics Informed Neural Network (PINN) Methodology for Coupled Moving Boundary PDEs](https://mlsanity.com/paper/2409.10910/) (2024)
- [Constitutive parameterized deep energy method for solid mechanics problems with random material parameters](https://mlsanity.com/paper/2603.26030/) (2026)

## Abstract (arXiv)

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.