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

TL;DR

The paper addresses the fragmented landscape between physics-based hydrology and data-driven ML by proposing physics-aware ML (PaML) as a unifying paradigm. It categorizes PaML into four modalities—physical data-guided ML, physics-informed ML, physics-embedded ML, and physics-aware hybrid learning—and systematically surveys their mechanisms, strengths, and limitations for rainfall-runoff and hydrodynamic processes. A key contribution is HydroPML, an open platform that operationalizes PaML for rainfall–runoff, flood forecasting, and hydrodynamic modeling, with real-world applicability demonstrated through landslide, flood forecasting, and runoff applications. The authors outline concrete future directions, including robust PaML-based hydro-solver development, data generation with generative models, improved parameterization and uncertainty quantification, and transferability to ungauged basins, all aimed at advancing toward a digital water cycle and Earth’s hydrological digital twin.

Abstract

Accurate hydrological understanding and water cycle prediction are crucial for addressing scientific and societal challenges associated with the management of water resources, particularly under the dynamic influence of anthropogenic climate change. Existing reviews predominantly concentrate on the development of machine learning (ML) in this field, yet there is a clear distinction between 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/.

Figures (6)

• Figure 1: (a) Examine the knowledge gap between physics-aware ML and hydrology in physics-aware ML from the keyword viewpoint. (b) Conceptual framework of physics-aware ML (PaML) and PaML-based hydrological application highlights. PaML includes physical data-guided ML, physics-informed ML, physics-embedded ML, and physics-aware hybrid learning.
• Figure 2: The proposed physics-aware machine learning (PaML) community.
• Figure 3: (a) Challenges of vanilla PINNs. (b) An example of vanilla PINNs failing to converge on high-frequency and multi-scale PDEs. 1-D convection equations with high-frequency (first row): Train and infer on a spatial-temporary resolution $256 \times 100$; 2-D steady incompressible Navier-Stokes equations (second row): Train and infer on a spatial resolution $49 \times 77$. Analytical solution and computational fluid dynamics (CFD) represent ground truth.
• Figure 4: Different hybrid approaches in physics-aware hybrid learning.
• Figure 5: The proposed process-based hydrology in physics-aware machine learning (HydroPML). HydroPML encompasses rainfall-runoff hydrological process understanding over time scales ranging from hours to decades and hydrodynamic process understanding over time scales from seconds to days. Red labels denote different objectives of HydroPML. For example, the oval labeled 1.1 represents short-term forecasts. The lower left and right corners represent the connections between PaML and the objects for rainfall-runoff hydrological processes and hydrodynamic processes, respectively. See the text for more detail.