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Advancing hydrological modeling requires simultaneous improvements in predictive skill and process understanding. While conceptual rainfall–runoff models remain widely used for their physical interpretability and reasonable robustness, their empirical flux formulations limits flexibility and generalizability across contrasting hydro-climatic conditions. Recent hybrid modeling studies [1,2] have shown that integrating neural networks or universal differential equations into conceptual models for flux correction can improve performance while preserving physical constraints. Following this perspective, we introduce a new modeling paradigm termed « neural reservoir », in which traditional empirical reservoir flux laws are replaced by physics–neural operators [3]. These operators are constructed by combining neural operators with shape functions derived from functional analysis of the original flux equations, ensuring mass balance and physically admissible bounds while remaining fully flexible and trainable. This framework enables the learning of internal water fluxes governing reservoir dynamics directly from data, while retaining the interpretability and structural consistency of reservoir-based models. Preliminary results show that the neural reservoir consistently outperforms both classical conceptual and purely data-driven LSTM benchmark models, while exhibiting physically meaningful behaviors and enhanced responsiveness to hydro-climatic variability. Ongoing work focuses on extending the evaluation to large-sample and national-scale settings, as well as on integrating additional data sources to further refine process representation. [1] Huynh, N. N. T., Garambois, P.-A., Renard, B., et al. (2025). A distributed hybrid physics–AI framework for learning corrections of internal hydrological fluxes and enhancing high-resolution regionalized flood modeling. Hydrol. Earth Syst. Sci., https://doi.org/10.5194/hess-29-3589-2025.[2] Huynh, N. N. T., Garambois, P.-A., Colleoni, F., et al. ( 2026). A hybrid physics–AI approach using universal differential equations with state-dependent neural networks for learnable, regionalizable, spatially distributed hydrological modeling. Geosci. Model Dev., https://doi.org/10.5194/gmd-19-1055-2026.[3] Huynh, N. N. T., Garambois, P.-A., Ettalbi, M., et al. (2026). Physics-Constrained Neural Reservoirs: A Powerful Neural Replacement of Conceptual Hydrological Laws for Learning Spatially Distributed Flow Dynamics. ESS Open Archive, https://doi.org/10.22541/essoar.177100580.07190684/v1.