PseudoSpectralNet: A hybrid neural differential equation for atmosphere models

When predicting complex systems such as parts of the Earth system, one typically relies on differential equations which often can be incomplete, missing unknown influences or include errors through their discretization. To remedy those effects, we present PseudoSpectralNet (PSN): a hybrid model that incorporates both a knowledge-based part of an atmosphere model and a data-driven part, an artificial neural network (ANN). PSN is a neural differential equation (NDE): it defines the right-hand side of a differential equation, combining a physical model with ANNs and is able to train its parameters inside this NDE. Similar to the approach of many atmosphere models, part of the model is computed in the spherical harmonics domain, and other parts in the grid domain. The model consists of ANN layers in each domain, information about derivatives, and parameters such as the orography. We demonstrate the capabilities of PSN on the well-studied Marshall Molteni Quasigeostrophic Model.