EGU General Assembly 2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

PseudoSpectralNet: A hybrid neural differential equation for atmosphere models

Maximilian Gelbrecht1,2 and Niklas Boers1,2,3
Maximilian Gelbrecht and Niklas Boers
  • 1TUM School of Engineering and Design, Technical University Munich, Munich, Germany (
  • 2Potsdam Institute for Climate Impact Research, Potsdam, Germany
  • 3Department of Mathematics and Global Systems Institute, University of Exeter, Exeter, UK

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.

How to cite: Gelbrecht, M. and Boers, N.: PseudoSpectralNet: A hybrid neural differential equation for atmosphere models, EGU General Assembly 2023, Vienna, Austria, 24–28 Apr 2023, EGU23-12403,, 2023.