# Inverse modeling of nonisothermal multiphase poromechanics using physics-informed neural networks

arXiv: https://arxiv.org/abs/2209.03276 · HTML: https://mlsanity.com/paper/2209.03276/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 87 references that are in the map.
- First posted on arXiv 7 Sep 2022.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Respecting causality is all you need for training physics-informed neural networks](https://mlsanity.com/paper/2203.07404/) (2022)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Physics informed deep learning for computational elastodynamics without labeled data](https://mlsanity.com/paper/2006.08472/) (2020)
- [Physics-informed deep learning for incompressible laminar flows](https://mlsanity.com/paper/2002.10558/) (2020)
- [Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture](https://mlsanity.com/paper/2011.13511/) (2020)
- [Likelihood-informed dimension reduction for nonlinear inverse problems](https://mlsanity.com/paper/1403.4680/) (2014)
- [Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training](https://mlsanity.com/paper/2110.03049/) (2021)
- [Physics-informed Neural Networks for Solving Nonlinear Diffusivity and Biot's equations](https://mlsanity.com/paper/2002.08235/) (2020)
- [Deep Learning for One-dimensional Consolidation](https://mlsanity.com/paper/2004.11689/) (2020)
- [Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problem](https://mlsanity.com/paper/2001.05172/) (2020)
- [Physics-informed neural network solution of thermo-hydro-mechanical (THM) processes in porous media](https://mlsanity.com/paper/2203.01514/) (2022)
- [Bayesian Poroelastic Aquifer Characterization from InSAR Surface Deformation Data. Part I: Maximum A Posteriori Estimate](https://mlsanity.com/paper/2002.10706/) (2020)
- [Physics-informed deep learning for flow and deformation in poroelastic media](https://mlsanity.com/paper/2010.15426/) (2020)

## Built on by (most cited first, 6 of 6)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Physics-Informed DeepONet Coupled with FEM for Convective Transport in Porous Media with Sharp Gaussian Sources](https://mlsanity.com/paper/2508.19847/) (2025)
- [Physics-informed Deep Learning to Solve Three-dimensional Terzaghi Consolidation Equation: Forward and Inverse Problems](https://mlsanity.com/paper/2401.05439/) (2024)
- [Network scaling and scale-driven loss balancing for intelligent poroelastography](https://mlsanity.com/paper/2411.08886/) (2024)
- [A novel Trunk Branch-net PINN for flow and heat transfer prediction in porous medium](https://mlsanity.com/paper/2501.16362/) (2025)
- [Physics-Inspired Deep Learning and Transferable Models for Bridge Scour Prediction](https://mlsanity.com/paper/2407.01258/) (2024)

## Abstract (arXiv)

We propose a solution strategy for parameter identification in multiphase thermo-hydro-mechanical (THM) processes in porous media using physics-informed neural networks (PINNs). We employ a dimensionless form of the THM governing equations that is particularly well suited for the inverse problem, and we leverage the sequential multiphysics PINN solver we developed in previous work. We validate the proposed inverse-modeling approach on multiple benchmark problems, including Terzaghi's isothermal consolidation problem, Barry-Mercer's isothermal injection-production problem, and nonisothermal consolidation of an unsaturated soil layer. We report the excellent performance of the proposed sequential PINN-THM inverse solver, thus paving the way for the application of PINNs to inverse modeling of complex nonlinear multiphysics problems.