# Using Machine Learning to Discover Parsimonious and Physically-Interpretable Representations of Catchment-Scale Rainfall-Runoff Dynamics

arXiv: https://arxiv.org/abs/2412.04845 · HTML: https://mlsanity.com/paper/2412.04845/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 133 references that are in the map.
- First posted on arXiv 6 Dec 2024.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A trans-disciplinary review of deep learning research for water resources scientists](https://mlsanity.com/paper/1712.02162/) (2017)
- [Low-rank lottery tickets: finding efficient low-rank neural networks via matrix differential equations](https://mlsanity.com/paper/2205.13571/) (2022)
- [Enhancing streamflow forecast and extracting insights using long-short term memory networks with data integration at continental scales](https://mlsanity.com/paper/1912.08949/) (2019)
- [From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling](https://mlsanity.com/paper/2007.15751/) (2020)
- [Network Augmentation for Tiny Deep Learning](https://mlsanity.com/paper/2110.08890/) (2021)
- [Minimum Description Length Recurrent Neural Networks](https://mlsanity.com/paper/2111.00600/) (2021)
- [Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracy](https://mlsanity.com/paper/2203.14827/) (2022)
- [MC-LSTM: Mass-Conserving LSTM](https://mlsanity.com/paper/2101.05186/) (2021)
- [Nowcasting-Nets: Deep Neural Network Structures for Precipitation Nowcasting Using IMERG](https://mlsanity.com/paper/2108.06868/) (2021)
- [A Mass-Conserving-Perceptron for Machine Learning-Based Modeling of Geoscientific Systems](https://mlsanity.com/paper/2310.08644/) (2023)
- [Rainfall-Runoff Prediction at Multiple Timescales with a Single Long Short-Term Memory Network](https://mlsanity.com/paper/2010.07921/) (2020)
- [Towards Interpretable Physical-Conceptual Catchment-Scale Hydrological Modeling using the Mass-Conserving-Perceptron](https://mlsanity.com/paper/2401.14521/) (2024)
- [Temporal Fusion Transformers for Streamflow Prediction: Value of Combining Attention with Recurrence](https://mlsanity.com/paper/2305.12335/) (2023)
- [Baseflow identification via explainable AI with Kolmogorov-Arnold networks](https://mlsanity.com/paper/2410.11587/) (2024)

## Built on by (most cited first, 4 of 4)

- [Scientific machine learning in Hydrology: a unified perspective](https://mlsanity.com/paper/2506.06308/) (2025)
- [Process-Aware AI for Rainfall-Runoff Modeling: A Mass-Conserving Neural Framework with Hydrological Process Constraints](https://mlsanity.com/paper/2603.25093/) (2026)
- [Improving Model Performance by Adapting the KGE Metric to Account for System Non-Stationarity](https://mlsanity.com/paper/2604.03906/) (2026)
- [A Gated Catchment Hydrology Model (GCHM) for Physically-Interpretable Rainfall-Evapotranspiration-Runoff Simulation Across Diverse Hydroclimatic Regimes](https://mlsanity.com/paper/2610.14493/) (2026)

## Abstract (arXiv)

Due largely to challenges associated with physical interpretability of machine learning (ML) methods, and because model interpretability is key to credibility in management applications, many scientists and practitioners are hesitant to discard traditional physical-conceptual (PC) modeling approaches despite their poorer predictive performance. Here, we examine how to develop parsimonious minimally-optimal representations that can facilitate better insight regarding system functioning. The term minimally-optimal indicates that the desired outcome can be achieved with the smallest possible effort and resources, while parsimony is widely held to support understanding. Accordingly, we suggest that ML-based modeling should use computational units that are inherently physically-interpretable, and explore how generic network architectures comprised of Mass-Conserving-Perceptron can be used to model dynamical systems in a physically-interpretable manner. In the context of spatially-lumped catchment-scale modeling, we find that both physical interpretability and good predictive performance can be achieved using a distributed-state network with context-dependent gating and information sharing across nodes. The distributed-state mechanism ensures a sufficient number of temporally-evolving properties of system storage while information-sharing ensures proper synchronization of such properties. The results indicate that MCP-based ML models with only a few layers (up to two) and relativity few physical flow pathways (up to three) can play a significant role in ML-based streamflow modelling.