Neural ODE Models in Large-Sample Hydrology

Abstract

Neural Ordinary Differential Equation (ODE) models have demonstrated high potential in providing accurate hydrologic predictions and process understanding for single catchments (Höge et al., 2022). Neural ODEs fuse a neural network model core with a mechanistic equation framework. This hybrid structure offers both traceability of model states and processes, like in conceptual hydrologic models, and the high flexibility of machine learning to learn and refine model interrelations. Aside of the functional dependence of internal processes on driving forces, like of evapotranspiration on temperature, Neural ODEs are also able to learn the effect of catchment-specific attributes, e.g. land cover types, on processes when being trained over multiple basins simultaneously. We demonstrate the performance of a generic Neural ODE architecture in a hydrologic large-sample setup with respect to both predictive accuracy and process interpretability. Using several hundred catchments, we show the capability of Neural ODEs to learn the general interplay of catchment-specific attributes and hydrologic drivers in order to predict discharge in out-of-sample basins. Further, we show how functional relations learned (encoded) by the neural network can be translated (decoded) into an interpretable form, and how this can be used to foster understanding of processes and the hydrologic system. Höge, M., Scheidegger, A., Baity-Jesi, M., Albert, C., & Fenicia, F.: Improving hydrologic models for predictions and process understanding using Neural ODEs. Hydrol. Earth Syst. Sci., 26, 5085-5102, https://hess.copernicus.org/articles/26/5085/2022/