# A Mass-Conserving-Perceptron for Machine Learning-Based Modeling of Geoscientific Systems

arXiv: https://arxiv.org/abs/2310.08644 · HTML: https://mlsanity.com/paper/2310.08644/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 134 references that are in the map.
- First posted on arXiv 12 Oct 2023.

## Builds on (most cited first, 22 of 22)

- [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)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [Interpretable Machine Learning -- A Brief History, State-of-the-Art and Challenges](https://mlsanity.com/paper/2010.09337/) (2020)
- [Towards Learning Universal, Regional, and Local Hydrological Behaviors via Machine-Learning Applied to Large-Sample Datasets](https://mlsanity.com/paper/1907.08456/) (2019)
- [A trans-disciplinary review of deep learning research for water resources scientists](https://mlsanity.com/paper/1712.02162/) (2017)
- [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)
- [A Survey on Physics Informed Reinforcement Learning: Review and Open Problems](https://mlsanity.com/paper/2309.01909/) (2023)
- [Physics-informed Dyna-Style Model-Based Deep Reinforcement Learning for Dynamic Control](https://mlsanity.com/paper/2108.00128/) (2021)
- [Nowcasting-Nets: Deep Neural Network Structures for Precipitation Nowcasting Using IMERG](https://mlsanity.com/paper/2108.06868/) (2021)
- [Prolongation of SMAP to Spatio-temporally Seamless Coverage of Continental US Using a Deep Learning Neural Network](https://mlsanity.com/paper/1707.06611/) (2017)
- [Node, Node-Link, and Node-Link-Group Diagrams: An Evaluation](https://mlsanity.com/paper/1404.1911/) (2014)
- [Differentiable modeling to unify machine learning and physical models and advance Geosciences](https://mlsanity.com/paper/2301.04027/) (2023)
- [Evaluating Catchment Models as Multiple Working Hypotheses: on the Role of Error Metrics, Parameter Sampling, Model Structure, and Data Information Content](https://mlsanity.com/paper/2009.00729/) (2020)
- [Neural Optimal Control using Learned System Dynamics](https://mlsanity.com/paper/2302.09846/) (2023)

## Built on by (most cited first, 7 of 7)

- [Towards Interpretable Physical-Conceptual Catchment-Scale Hydrological Modeling using the Mass-Conserving-Perceptron](https://mlsanity.com/paper/2401.14521/) (2024)
- [Using Machine Learning to Discover Parsimonious and Physically-Interpretable Representations of Catchment-Scale Rainfall-Runoff Dynamics](https://mlsanity.com/paper/2412.04845/) (2024)
- [Scientific machine learning in Hydrology: a unified perspective](https://mlsanity.com/paper/2506.06308/) (2025)
- [Knowledge distillation as a pathway toward next-generation intelligent ecohydrological modeling systems](https://mlsanity.com/paper/2509.01972/) (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)

Although decades of effort have been devoted to building Physical-Conceptual (PC) models for predicting the time-series evolution of geoscientific systems, recent work shows that Machine Learning (ML) based Gated Recurrent Neural Network technology can be used to develop models that are much more accurate. However, the difficulty of extracting physical understanding from ML-based models complicates their utility for enhancing scientific knowledge regarding system structure and function. Here, we propose a physically-interpretable Mass Conserving Perceptron (MCP) as a way to bridge the gap between PC-based and ML-based modeling approaches. The MCP exploits the inherent isomorphism between the directed graph structures underlying both PC models and GRNNs to explicitly represent the mass-conserving nature of physical processes while enabling the functional nature of such processes to be directly learned (in an interpretable manner) from available data using off-the-shelf ML technology. As a proof of concept, we investigate the functional expressivity (capacity) of the MCP, explore its ability to parsimoniously represent the rainfall-runoff (RR) dynamics of the Leaf River Basin, and demonstrate its utility for scientific hypothesis testing. To conclude, we discuss extensions of the concept to enable ML-based physical-conceptual representation of the coupled nature of mass-energy-information flows through geoscientific systems.