Applications of physics-informed neural networks in fluid flow in porous media - A review study

Physics-informed neural networks have moved quickly from small proof-of-concept studies to a serious line of research for subsurface flow problems, especially where heterogeneity, sparse observations, and many-query workflows make conventional simulation expensive. This review examines how these methods have been used in porous-media applications relevant to reservoir engineering, carbon storage, and related energy systems, covering early Darcy- and Richards-equation studies as well as later work on two-phase displacement, fractured formations, inverse problems, and coupled thermo-hydro-mechanical settings. Rather than simply cataloging applications, we compare the main methodological responses to the field’s recurring difficulties, including adaptive sampling, conservative and mixed formulations, domain decomposition, discretization-aware architectures, and operator-learning surrogates. The literature points to a clear shift away from a one-method-fits-all view: classical physics-informed neural networks, extended variants, and broader physics-informed surrogates are proving useful for different tasks depending on discontinuities, computational scale, and deployment needs. At the same time, several barriers remain unresolved, notably training instability, three-dimensional scalability, uncertainty quantification, validation against laboratory and field-relevant data, and integration with established industrial simulators. We therefore frame the current state of the field not only as a record of progress, but also as a practical guide to method selection and future development in porous-media energy applications. • Physics-informed neural networks are compared across porous flow applications. • Review covers Darcy flow, transport, fractures, and coupled subsurface processes. • Tables and a new taxonomy link modeling challenges to suitable neural methods. • Practical guidance emphasizes validation and integration with reservoir simulators. • Open challenges include scale-up, uncertainty, and industrial deployment.