Scientific machine learning in Hydrology: a unified perspective

TL;DR

This paper reviews and unifies various scientific machine learning approaches in hydrology, providing a structured framework to enhance understanding, assessment, and future research directions in the field.

Contribution

It introduces a unified conceptual framework for different SciML families in hydrology, addressing fragmentation and fostering cumulative progress.

Findings

Unified framework clarifies methodological distinctions

Highlights limitations and future opportunities in SciML for hydrology

Supports systematic research and method assessment

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.