# Towards Interpretable Physical-Conceptual Catchment-Scale Hydrological Modeling using the Mass-Conserving-Perceptron

arXiv: https://arxiv.org/abs/2401.14521 · HTML: https://mlsanity.com/paper/2401.14521/

## Key facts

- Cited by 4 papers in the map (data through 7 Oct 2026).
- Builds on 17 of its 124 references that are in the map.
- First posted on arXiv 25 Jan 2024.

## Builds on (most cited first, 17 of 17)

- [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)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Towards Learning Universal, Regional, and Local Hydrological Behaviors via Machine-Learning Applied to Large-Sample Datasets](https://mlsanity.com/paper/1907.08456/) (2019)
- [Physics Guided RNNs for Modeling Dynamical Systems: A Case Study in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/1810.13075/) (2018)
- [SPIGAN: Privileged Adversarial Learning from Simulation](https://mlsanity.com/paper/1810.03756/) (2018)
- [Deep Learning of Subsurface Flow via Theory-guided Neural Network](https://mlsanity.com/paper/1911.00103/) (2019)
- [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)
- [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)
- [Enhancing predictive skills in physically-consistent way: Physics Informed Machine Learning for Hydrological Processes](https://mlsanity.com/paper/2104.11009/) (2021)
- [A Mass-Conserving-Perceptron for Machine Learning-Based Modeling of Geoscientific Systems](https://mlsanity.com/paper/2310.08644/) (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)
- [Fast-Slow Streamflow Model Using Mass-Conserving LSTM](https://mlsanity.com/paper/2107.06057/) (2021)
- [A Gaussian Sliding Windows Regression Model for Hydrological Inference](https://mlsanity.com/paper/2306.00453/) (2023)

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

- [Using Machine Learning to Discover Parsimonious and Physically-Interpretable Representations of Catchment-Scale Rainfall-Runoff Dynamics](https://mlsanity.com/paper/2412.04845/) (2024)
- [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)

## Abstract (arXiv)

We investigate the applicability of machine learning technologies to the development of parsimonious, interpretable, catchment-scale hydrologic models using directed-graph architectures based on the mass-conserving perceptron (MCP) as the fundamental computational unit. Here, we focus on architectural complexity (depth) at a single location, rather than universal applicability (breadth) across large samples of catchments. The goal is to discover a minimal representation (numbers of cell-states and flow paths) that represents the dominant processes that can explain the input-state-output behaviors of a given catchment, with particular emphasis given to simulating the full range (high, medium, and low) of flow dynamics. We find that a HyMod Like architecture with three cell-states and two major flow pathways achieves such a representation at our study location, but that the additional incorporation of an input-bypass mechanism significantly improves the timing and shape of the hydrograph, while the inclusion of bi-directional groundwater mass exchanges significantly enhances the simulation of baseflow. Overall, our results demonstrate the importance of using multiple diagnostic metrics for model evaluation, while highlighting the need for properly selecting and designing the training metrics based on information-theoretic foundations that are better suited to extracting information across the full range of flow dynamics. This study sets the stage for interpretable regional-scale MCP-based hydrological modeling (using large sample data) by using neural architecture search to determine appropriate minimal representations for catchments in different hydroclimatic regimes.