# Physics-informed neural network solution of thermo-hydro-mechanical (THM) processes in porous media

arXiv: https://arxiv.org/abs/2203.01514 · HTML: https://mlsanity.com/paper/2203.01514/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 65 references that are in the map.
- First posted on arXiv 3 Mar 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain](https://mlsanity.com/paper/2004.13145/) (2020)
- [Efficient training of physics-informed neural networks via importance sampling](https://mlsanity.com/paper/2104.12325/) (2021)
- [Physics informed deep learning for computational elastodynamics without labeled data](https://mlsanity.com/paper/2006.08472/) (2020)
- [Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equations](https://mlsanity.com/paper/2107.10711/) (2021)
- [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)
- [DiscretizationNet: A Machine-Learning based solver for Navier-Stokes Equations using Finite Volume Discretization](https://mlsanity.com/paper/2005.08357/) (2020)
- [Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training](https://mlsanity.com/paper/2110.03049/) (2021)
- [A nonlocal physics-informed deep learning framework using the peridynamic differential operator](https://mlsanity.com/paper/2006.00446/) (2020)
- [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)
- [Learning Unknown Physics of non-Newtonian Fluids](https://mlsanity.com/paper/2009.01658/) (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, 8 of 8)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method](https://mlsanity.com/paper/2206.13103/) (2022)
- [Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domains](https://mlsanity.com/paper/2302.04954/) (2023)
- [Inverse modeling of nonisothermal multiphase poromechanics using physics-informed neural networks](https://mlsanity.com/paper/2209.03276/) (2022)
- [Learning Generic Solutions for Multiphase Transport in Porous Media via the Flux Functions Operator](https://mlsanity.com/paper/2307.01354/) (2023)
- [Bridging Data and Physics: A Graph Neural Network-Based Hybrid Twin Framework](https://mlsanity.com/paper/2512.15767/) (2025)
- [STONet: A neural operator for modeling solute transport in micro-cracked reservoirs](https://mlsanity.com/paper/2412.05576/) (2024)
- [A novel Trunk Branch-net PINN for flow and heat transfer prediction in porous medium](https://mlsanity.com/paper/2501.16362/) (2025)

## Abstract (arXiv)

Physics-Informed Neural Networks (PINNs) have received increased interest for forward, inverse, and surrogate modeling of problems described by partial differential equations (PDE). However, their application to multiphysics problem, governed by several coupled PDEs, present unique challenges that have hindered the robustness and widespread applicability of this approach. Here we investigate the application of PINNs to the forward solution of problems involving thermo-hydro-mechanical (THM) processes in porous media, which exhibit disparate spatial and temporal scales in thermal conductivity, hydraulic permeability, and elasticity. In addition, PINNs are faced with the challenges of the multi-objective and non-convex nature of the optimization problem. To address these fundamental issues, we: (1)~rewrite the THM governing equations in dimensionless form that is best suited for deep-learning algorithms; (2)~propose a sequential training strategy that circumvents the need for a simultaneous solution of the multiphysics problem and facilitates the task of optimizers in the solution search; and (3)~leverage adaptive weight strategies to overcome the stiffness in the gradient flow of the multi-objective optimization problem. Finally, we apply this framework to the solution of several synthetic problems in 1D and~2D.