Physics-Informed Machine Learning in Hydrology and Water Resources: A Systematic Bibliometric Analysis

George Kwame Frimpong, Omer Mermer , Ibrahim Demir

This study presents a systematic bibliometric review of Physics-Informed Machine Learning (PIML) research in hydrology and water resources, examining the field's evolution in response to the limitations of traditional process-based models and data-driven approaches. Using a PRISMA-guided framework and a curated dataset from the Scopus database, the analysis evaluated publication trends, leading publication venues, national specialization patterns, international collaboration networks, and emerging research themes. The results reveal a rapidly expanding and increasingly collaborative field, led primarily by China and the United States, with applications concentrated in areas characterized by complex physical processes and limited data availability, particularly flood and disaster management and groundwater modeling and management. Citation patterns highlight the importance of physically consistent prediction and computationally efficient surrogate modeling as major drivers of the field's growth. Despite significant progress, challenges remain, including sensitivity to heterogeneous data, model transferability, and geographical disparities in research participation. Emerging advances in differentiable modeling, multimodal physics-informed frameworks, and domain-specific foundation models are expected to shape the next generation of hydrological intelligence systems. Overall, the findings demonstrate that PIML is becoming an increasingly important paradigm for developing physically consistent, interpretable, and scalable solutions to contemporary water resources and climate resilience challenges.