DeepDiscover: towards autonomous discovery of bucket-type conceptual models – a proof of concept applied to hydrology

• DeepDiscover autonomously discovers bucket-type conceptual hydrological models. • DeepDiscover outperforms conceptual, PeML, and deep learning benchmarks. • DeepDiscover learns processes and states consistent with EXP-HYDRO dynamics. • DeepDiscover exhibits physically coherent and causally consistent responses. • DeepDiscover infers hydrological processes without expert-defined equations. Conceptual hydrological models are widely used to represent rainfall-runoff dynamics at the catchment scale. However, their structure and governing equations are traditionally defined a priori by a human expert. This reliance on expert-defined formulations limits scalability, constrains structural diversity, and hampers the systematic exploration of alternative process representations. In this study, we introduce DeepDiscover, a framework designed to autonomously infer bucket-type conceptual hydrological models from data within a physics-embedded machine learning (PeML) setting. The approach relies on a modular neural architecture composed of elementary units intended to represent reservoirs within bucket-type conceptual models. In this architecture, hydrological processes are not explicitly prescribed but are learned implicitly under explicit physical constraints. DeepDiscover is evaluated on the CAMELS-US dataset in a streamflow prediction task through three complementary experiments. In the first experiment, predictive performance is assessed against several benchmark models: EXP-HYDRO (conceptual model), EXP-PeML, a 1D-CNN, and an LSTM, all trained under identical sequence-to-sequence conditions. The DeepDiscover-based model (DD-PeML) outperforms all benchmarks, achieving median NSE and KGE values of 0.68 and 0.70, respectively, on the test set. The second experiment investigates whether DeepDiscover can recover hydrologically meaningful internal dynamics when trained to mirror EXP-HYDRO. The inferred process and state variables closely match those of EXP-HYDRO, with median R 2 of approximately 70 % for processes and 80 % for states. An additional exploratory analysis increases the number of candidate processes, showing that the learned fluxes can still be consistently associated with known hydrological process types, supporting the framework’s capacity for data-driven process discovery. Finally, perturbation experiments demonstrate physically coherent responses to changes in precipitation and temperature, confirming that the learned dynamics remain consistent with fundamental hydrological behavior. Overall, this work demonstrates that autonomous inference of bucket-type conceptual hydrological models from data is feasible within a physically constrained learning framework, and represents a step toward reducing dependence on expert-defined model formulations.