EGU General Assembly 2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Neural Partial Differential Equations for Simple Climate Models 

Maximilian Gelbrecht1,2,3, Niklas Boers1,3,4, and Jürgen Kurths1,2,5
Maximilian Gelbrecht et al.
  • 1Potsdam Institute for Climate Impact Research, Research Domain IV, Potsdam, Germany (
  • 2Physics Department, Humboldt University Berlin
  • 3Department of Mathematics and Computer Science, Freie Universität Berlin
  • 4Department of Mathematics and Global Systems Institute, University of Exeter
  • 5Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia

When predicting complex systems such as parts of the Earth system, one typically relies on differential equations which can often be incomplete, missing unknown influences or higher order effects. By augmenting the equations with artificial neural networks we can compensate these deficiencies. The resulting hybrid models are also known as universal differential equations. We show that this can be used to predict the dynamics of high-dimensional chaotic partial differential equations, such as the ones describing atmospheric dynamics, even when only short and incomplete training data are available. In a first step towards a hybrid atmospheric model, simplified, conceptual atmospheric models are used in synthetic examples where parts of the governing equations are replaced with artificial neural networks. The forecast horizon for these high dimensional systems is typically much larger than the training dataset, showcasing the large potential of the approach. 

How to cite: Gelbrecht, M., Boers, N., and Kurths, J.: Neural Partial Differential Equations for Simple Climate Models , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8262,, 2021.


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