Improving hydrologic models for predictions and process understanding using neural ODEs

Abstract. Deep learning methods have frequently outperformed conceptual hydrologic models in rainfall-runoff modelling. Attempts of investigating such deep learning models internally are being made, but the traceability of model states and processes and their interrelations to model input and output is not yet fully understood. Direct interpretability of mechanistic processes has always been considered an asset of conceptual models that helps to gain system understanding aside of predictability. We introduce hydrologic neural ordinary differential equation (ODE) models that perform as well as state-of-the-art deep learning methods in stream flow prediction while maintaining the ease of interpretability of conceptual hydrologic models. In neural ODEs, internal processes that are represented in differential equations, are substituted by neural networks. Therefore, neural ODE models enable the fusion of deep learning with mechanistic modelling. We demonstrate the basin-specific predictive performance for 569 catchments of the continental United States. For exemplary basins, we analyse the dynamics of states and processes learned by the model-internal neural networks. Finally, we discuss the potential of neural ODE models in hydrology.