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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. Plain Language Summary: We show that conventional machine learning technologies can be used to develop parsimonious, interpretable, catchment‐scale hydrologic models using the mass‐conserving perceptron (MCP) as a fundamental computational unit. Using data from the Leaf River Basin, we test a variety of minimal, dominant process, representations that can explain the input‐state‐output dynamics of the catchment. Our results demonstrate the importance of using multiple diagnostic metrics for evaluation and comparison of different model architectures, and highlight the importance of choosing (or designing) objective functions for model training that are properly suited to the task of extracting information across the full range of flow dynamics. This depth‐focus 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. Key Points: We utilize mass‐conserving perceptron (MCP) directed‐graph architectures to develop concise, interpretable catchment‐scale hydrologic modelsWe focus on model complexity (depth) at a single location, rather than universal applicability (breadth) across large samples of catchmentsThis study set the stage for interpretable MCP‐based modeling to find minimal representations in different hydroclimatic regimes [ABSTRACT FROM AUTHOR]

We propose a method for calculating the non-radiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface (PES) in the Franck-Condon region. The method combines the n-mode representation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method (TD-DMRG) to simulate quantum dynamics. In addition, in the framework of TD-DMRG, we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process. We use this method to study the internal conversion (IC) process of azulene after taking into account the anharmonicity of the ground state PES. The results show that even for this semi-rigid molecule, the intramode anharmonicity enhances the IC rate significantly, and after considering the two-mode coupling effect, the rate increases even further. The reason is that the anharmonicity enables the C–H vibrations to receive electronic energy while C–H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0. [ABSTRACT FROM AUTHOR]