From hydrological laws to catchment models: A process-based model matches deep-learning accuracy on three continents

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   Effective catchment hydrologic representations are low-dimensional but interaction-dependent

   Yuan-Heng Wang, Hoshin V. Gupta · 2026 · Not summarized yet

   This study tests how low-dimensional, mass-conserving catchment models gain predictive skill from additional states and interactions across US catchments.

   Abstract

   Hydrologic models must reconcile predictive flexibility with physical interpretability, yet the complexity required to reproduce catchment dynamics remains uncertain. Here we compare conceptual hydrologic models and neural networks built from mass-conserving computational units across 513 catchments in the contiguous United States, varying state dimensionality and cross-state information sharing. Under likelihood-based selection, median testing-period Kling-Gupta efficiency skill score (KGEss) increases from 0.83 with one allowable state to 0.89 with two, but reaches only 0.90 with five. KGE-based selection shows similarly rapid saturation. Cross-state information sharing provides an additio…

2. Close Another approach to the problem Not relevant

   Differentiable, Learnable, Regionalized Process‐Based Models With Multiphysical Outputs can Approach State‐Of‐The‐Art Hydrologic Prediction Accuracy

   D. Feng, Jiang-Tao Liu, K. Lawson et al. · 2022 · Water Resources Research · cited 274 times · Not summarized yet

   The δ models combine differentiable process-based structures with regionalized parameters to approach LSTM streamflow accuracy and predict additional water-cycle variables.

   Abstract

   Predictions of hydrologic variables across the entire water cycle have significant value for water resources management as well as downstream applications such as ecosystem and water quality modeling. Recently, purely data‐driven deep learning models like long short‐term memory (LSTM) showed seemingly insurmountable performance in modeling rainfall runoff and other geoscientific variables, yet they cannot predict untrained physical variables and remain challenging to interpret. Here, we show that differentiable, learnable, process‐based models (called δ models here) can approach the performance level of LSTM for the intensively observed variable (streamflow) with regionalized parameterizatio…

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   Process-Aware AI for Rainfall-Runoff Modeling: A Mass-Conserving Neural Framework with Hydrological Process Constraints

   M. Farmani, Hoshin V. Gupta, A. Behrangi et al. · 2026 · arXiv.org · preprint, not peer reviewed · Not summarized yet

   The Mass-Conserving Perceptron incrementally adds hydrological process representations to a conservation-constrained neural framework for rainfall-runoff prediction.

   Abstract

   Machine learning models can achieve high predictive accuracy in hydrological applications but often lack physical interpretability. The Mass-Conserving Perceptron (MCP) provides a physics-aware artificial intelligence (AI) framework that enforces conservation principles while allowing hydrological process relationships to be learned from data. In this study, we investigate how progressively embedding physically meaningful representations of hydrological processes within a single MCP storage unit improves predictive skill and interpretability in rainfall-runoff modeling. Starting from a minimal MCP formulation, we sequentially introduce bounded soil storage, state-dependent conductivity, vari…

4. Close Broader context Not relevant

   When physics gets in the way: an entropy-based evaluation of conceptual constraints in hybrid hydrological models

   Manuel Álvarez Chaves, Eduardo Acuña Espinoza, Uwe Ehret et al. · 2026 · Hydrology and Earth System Sciences · cited 2 times · Not summarized yet

   This study evaluates how conceptual physical constraints affect hybrid hydrological model behavior using an entropy-based approach.

   Abstract

   Abstract. Merging physics-based with data-driven approaches in hybrid hydrological modeling offers new opportunities to enhance predictive accuracy while addressing challenges of model interpretability and fidelity. Traditional hydrological models, developed using physical principles, are easily interpretable but often limited by their rigidity and assumptions. In contrast, machine learning methods, such as Long Short-Term Memory (LSTM) networks, offer exceptional predictive performance but are often criticized for their black-box nature. Hybrid models aim to reconcile these approaches by imposing physics to constrain and understand what the ML part of the model does. This study introduces a…

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   Distributed Hydrological Modeling With Physics‐Encoded Deep Learning: A General Framework and Its Application in the Amazon

   Chao Wang, Shi-Jie Jiang, Yi Zheng et al. · 2024 · Water Resources Research · cited 103 times · Not summarized yet

   This framework combines a distributed process-based model with neural parameter mapping and learned replacements for uncertain processes in the Amazon.

   Abstract

   While deep learning (DL) models exhibit superior simulation accuracy over traditional distributed hydrological models (DHMs), their main limitations lie in opacity and the absence of underlying physical mechanisms. The pursuit of synergies between DL and DHMs is an engaging research domain, yet a definitive roadmap remains elusive. In this study, a novel framework that seamlessly integrates a process‐based hydrological model encoded as a neural network (NN), an additional NN for mapping spatially distributed and physically meaningful parameters from watershed attributes, and NN‐based replacement models representing inadequately understood processes is developed. Multi‐source observations are…

6. Close Broader context Not relevant

   Hydrological Concept Formation inside Long Short-Term Memory (LSTM) networks

   Thomas Lees, S. Reece, Frederik Kratzert et al. · 2021 · Hydrology and Earth System Sciences · cited 196 times · Not summarized yet

   This study interprets LSTM internal states to examine whether their learned rainfall-runoff relationships represent hydrological concepts.

   Abstract

   Abstract. Neural networks have been shown to be extremely effective rainfall-runoff models, where the river discharge is predicted from meteorological inputs. However, the question remains, what have these models learned? Is it possible to extract information about the learned relationships that map inputs to outputs? And do these mappings represent known hydrological concepts? Small-scale experiments have demonstrated that the internal states of Long Short-Term Memory Networks (LSTMs), a particular neural network architecture predisposed to hydrological modelling, can be interpreted. By extracting the tensors which represent the learned translation from inputs (precipitation, temperature) t…

7. Close Same question Not relevant

   Rainfall-Runoff Simulation and Interpretation in Great Britain using LSTMs

   Thomas Lees, M. Buechel, B. Anderson et al. · 2021 · Not summarized yet

   This study evaluates LSTM and entity-aware LSTM rainfall-runoff predictions across British catchments and interprets their simulated hydrological processes.

   Abstract

   <p>Techniques from the field of machine learning have shown considerable promise in rainfall-runoff modelling. This research offers three novel contributions to the advancement of this field: a study of the performance of LSTM based models in a GB hydrological context; a diagnosis of hydrological processes that data-driven models simulate well but conceptual models struggle with; and finally an exploration of methods for interpreting the internal cell states of the LSTMs.&#160;</p><p>In this study we train two deep learning models, a Long Short Term Memory (LSTM) Network and an Entity Aware LSTM (EALSTM), to simulate discharge for 518 catchments across Great Britain using a newly published d…

8. Close Same method, another problem Not relevant

   The suitability of differentiable, physics-informed machine learning hydrologic models for ungauged regions and climate change impact assessment

   D. Feng, H. Beck, K. Lawson et al. · 2023 · Hydrology and Earth System Sciences · cited 178 times · Not summarized yet

   This study uses regionalized differentiable process-based models to test streamflow predictions in ungauged regions and under climate change.

   Abstract

   Abstract. As a genre of physics-informed machine learning, differentiable process-based hydrologic models (abbreviated as δ or delta models) with regionalized deep-network-based parameterization pipelines were recently shown to provide daily streamflow prediction performance closely approaching that of state-of-the-art long short-term memory (LSTM) deep networks. Meanwhile, δ models provide a full suite of diagnostic physical variables and guaranteed mass conservation. Here, we ran experiments to test (1) their ability to extrapolate to regions far from streamflow gauges and (2) their ability to make credible predictions of long-term (decadal-scale) change trends. We evaluated the models bas…