Physics-Informed Machine Learning in Subsurface Multiphysics Flow Modeling: Integrating Physical Constraints for Accelerated Simulation

Abstract

Subsurface thermo-hydro-mechanical (THM) coupled processes are fundamental to geomechanics, yet conventional mesh-based methods face high computational costs and limited efficiency in strongly nonlinear simulations and inverse problems. This review examines two representative physics-informed machine learning paradigms for THM modeling: physics-informed neural networks (PINNs) and neural operators (NOs). Relevant studies were identified through iterative keyword-based searches and citation tracking and were comparatively analyzed in terms of physical embedding, data dependence, computational efficiency, inverse capability, generalization, and engineering applications. The analysis shows that PINNs are well suited to physics-constrained simulation and parameter inversion from sparse data but are limited by training instability and loss imbalance. NOs enable rapid repeated forward predictions but depend strongly on representative training data and may perform poorly under out-of-distribution conditions. This review clarifies the complementary roles, trade-offs, and application boundaries of PINNs and NOs and highlights their hybrid integration as a promising route toward efficient and physically consistent subsurface THM simulation.