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

arXiv: https://arxiv.org/abs/2310.05227 · HTML: https://mlsanity.com/paper/2310.05227/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 145 of its 367 references that are in the map.
- First posted on arXiv 8 Oct 2023.

## Builds on (most cited first, 30 of 145)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Transformers in Vision: A Survey](https://mlsanity.com/paper/2101.01169/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [A Survey on Visual Transformer](https://mlsanity.com/paper/2012.12556/) (2020)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)

## Built on by (most cited first, 11 of 11)

- [On the Foundations of Earth and Climate Foundation Models](https://mlsanity.com/paper/2405.04285/) (2024)
- [Knowledge-guided Machine Learning: Current Trends and Future Prospects](https://mlsanity.com/paper/2403.15989/) (2024)
- [Large-scale flood modeling and forecasting with FloodCast](https://mlsanity.com/paper/2403.12226/) (2024)
- [Beyond Grid Data: Exploring Graph Neural Networks for Earth Observation](https://mlsanity.com/paper/2411.03223/) (2024)
- [Aligning Perception, Reasoning, Modeling and Interaction: A Survey on Physical AI](https://mlsanity.com/paper/2510.04978/) (2025)
- [A review of unsupervised learning in astronomy](https://mlsanity.com/paper/2406.17316/) (2024)
- [Physics-embedded Fourier Neural Network for Partial Differential Equations](https://mlsanity.com/paper/2407.11158/) (2024)
- [SD-PSFNet: Sequential and Dynamic Point Spread Function Network for Image Deraining](https://mlsanity.com/paper/2511.17993/) (2025)
- [Scientific machine learning in Hydrology: a unified perspective](https://mlsanity.com/paper/2506.06308/) (2025)
- [Topology enables learning-based hydrodynamic prediction of the global river system](https://mlsanity.com/paper/2602.22293/) (2026)
- [Real-Time State-of-Health Estimation and Online Degradation Prognosis from Partial Battery Discharge Using Physics-Informed Neural Networks](https://mlsanity.com/paper/2608.14764/) (2026)

## Abstract (arXiv)

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/.