Physics-informed neural networks for groundwater: evidence, limits, and a roadmap

Physics-informed neural networks (PINNs) have recently emerged as a promising machine learning paradigm that embeds physical laws into data-driven modeling, offering new opportunities for addressing long-standing challenges in groundwater science. Distinct from previous reviews, this study presents a dual-track framework that integrates bibliometric analysis with critical methodological synthesis to systematically review 178 articles published between 2019 and 2025 in the Web of Science Core Collection. The results show that current research hotspots center on groundwater flow and seepage simulation, multi-physics coupling, parameter inversion, and the characterization of porous media flow processes, with a clear shift from idealized synthetic cases toward more complex heterogeneous aquifer applications. Furthermore, this review summarizes the major strengths of PINNs in groundwater applications and identifies key methodological bottlenecks related to training stability, computational efficiency, boundary condition enforcement, and cross-scenario generalization. Building on these insights, a development roadmap is proposed to advance PINNs in groundwater science, emphasizing weak-form formulations, neural operators, hybrid physics–numerical solvers, high-performance computing, and integrated frameworks for multi-source data fusion and uncertainty quantification. These directions provide guidance for evolving PINNs into scalable and reliable tools for groundwater modeling and management.