Scientific machine learning in Hydrology: a unified perspective

Abstract

Scientific machine learning (SciML) provides a structured approach to integrating physical knowledge into data-driven modeling, offering significant potential for advancing hydrological research. In recent years, multiple methodological families have emerged, including physics-informed machine learning, physics-guided machine learning, hybrid physics-machine learning, and data-driven physics discovery. Within each of these families, a proliferation of heterogeneous approaches has developed independently, often without conceptual coordination. This fragmentation complicates the assessment of methodological novelty and makes it difficult to identify where meaningful advances can still be made in the absence of a unified conceptual framework. This review, the first focused overview of SciML in hydrology, addresses these limitations by proposing a unified methodological framework for each SciML family, bringing together representative contributions into a coherent structure that fosters conceptual clarity and supports cumulative progress in hydrological modeling. Finally, we highlight the limitations and future opportunities of each unified family to guide systematic research in hydrology, where these methods remain underutilized.

References in corpus (11)

• A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
• Differentiable modeling to unify machine learning and physical models and advance Geosciences
• Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons
• Efficient training of physics-informed neural networks via importance sampling
• Interpretable Scientific Discovery with Symbolic Regression: A Review
• Physics guided machine learning using simplified theories
• Physics-informed neural networks of the Saint-Venant equations for downscaling a large-scale river model
• Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics
• Accelerating hydrodynamic simulations of urban drainage systems with physics-guided machine learning
• Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication
• A Robust Learning Methodology for Uncertainty-aware Scientific Machine Learning models