Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology

Aug 4, 2026

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Accurate understanding of geoscientific processes and reliable water-cycle prediction underpin solutions to water-resource challenges affecting both science and society. Prior reviews mainly cover machine learning in this domain, while process-based hydrology and ML are treated as distinct paradigms. This work proposes physics-aware ML to bridge the gap, integrating prior physical knowledge or physics-based modeling into ML, and reviews methods grouped into physics data-guided, physics-informed, physics-embedded, and physics-aware hybrid learning. A PaML-based hydrology platform, HydroPML, is released to improve explainability and causality and support realization of a digital water cycle.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages44

Reading Time1 h 51 min

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Abstract

Introduction

arXiv :2310 .05227v 5 [ cs .LG] 12 Jul 2024 Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology Qingsong Xu 1 , Yilei Shi3 , Jonathan Bamber 1,6 , Ye Tuo4 , Ralf Ludwig5 , and Xiao Xiang Zhu 1,2 1 Data Science in Earth Observation, Technical University of Munich, Munich, Germany 2 Munich Center for Machine Learning, Munich, Germany 3 School of Engineering and Design, Technical University of Munich, Munich, Germany 4 Hydrology and River Basin Management, Technical University of Munich, Munich, Germany 5 Department of Geography, Ludwig-Maximilians-University, Munich, Germany 6 School of Geographical Sciences, University of Bristol, UK ABSTRACT Accurate geoscientific process understanding and water cycle prediction are crucial for addressing scientific and societal challenges associated with the management of water resources. Existing reviews predominantly concentrate on the development of machine learning (ML) in this field, yet there is a clear distinction between process-based hydrology and ML as separate paradigms. Here, we introduce physics-aware ML as a transformative approach to overcome the perceived barrier and revolutionize both fields. Specifically, we present a comprehensive review of the physics-aware ML methods, building a structured community (PaML) of existing methodologies that integrate prior physical knowledge or physics-based modeling into ML. We systematically analyze these PaML methodologies with respect to four aspects: physical data-guided ML, physics-informed ML, physics-embedded ML, and physics-aware hybrid learning. PaML facilitates ML-aided hypotheses, accelerating insights from big data and fostering scientific discoveries. We first conduct a systematic review of hydrology in PaML, including rainfall-runoff hydrological processes and hydrodynamic processes, and highlight the most promising and challenging directions for different objectives and PaML methods. Finally, a new PaML-based hydrology platform, termed HydroPML, is released as a foundation for hydrological applications. HydroPML enhances the explainability and causality of ML and lays the groundwork for the digital water cycle’s realization. The HydroPML platform is publicly available at [https://hydropml.github.io/](https://hydropml.github.io/) . 1 Introduction Numerous scientific and societal challenges associated with understanding and preparing for environmental change rest upon our ability to understand and predict water cycle changes 1. Process-based hydrological models play a crucial role in understanding and managing the Earth’s water resources2 and planning for water security and managing extremes such as floods and droughts3. Many hydrological processes can be described as complex physical dynamics spanning various spatial and temporal scales, such as hydrodynamic processes and rainfall-runoff processes. Physical methods have been highly effective in elucidating and forecasting the state changes in a hydrological process4. However, process-based hydrology continues to present important challenges 1. (1) A subset of process-based hydrological methods requires significant computational resources and expertise. For example, a global flood solver requires dramatic computational resources based on a traditional finite difference solver5. (2) Process-based hydrological models encounter limitations due to existing knowledge gaps. For example, the two-way feedback between humans and water systems is physically agnostic, but it is crucial for the water cycles6, 7. A new paradigm is needed to reduce knowledge gaps and explore the unknowns. (3) Process-based hydrology models frequently struggle to rapidly exploit the information in big data. For example, abundant remote sensing observations and hydrological measurements can be utilized for parameter calibration by reducing the differences between model predictions and these big data. However, most traditional

FAQs

Why are process-based hydrological models important, and what challenges do they face?

They are crucial for understanding and managing Earth’s water resources and for planning water security and extremes like floods and droughts. Key challenges include high computational demands, knowledge gaps that limit physical representation, and difficulty exploiting big-data information efficiently due to uncertainty and costly iterative calibration.

What limitations arise from purely data-driven machine learning in hydrology?

Data-driven ML can struggle with nonlinear and chaotic dynamics, fail to maintain physical consistency without explicit constraints, and generalize poorly under distribution shifts. It also often lacks interpretability and causal grounding, reducing trust when conditions change.

How does physics-aware machine learning address the gap between hydrology and ML?

It integrates prior physical knowledge or physics-based modeling into ML, reducing the barrier between process-based hydrology and data-driven approaches. The document reviews physics-aware ML methods and organizes them into categories such as physics data-guided, physics-informed, physics-embedded, and physics-aware hybrid learning.

Aug 4, 2026

Upload by Liam