Neural partial differential equations for chaotic systems

Maximilian Gelbrecht, Niklas Boers, Jurgen Kurths

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


When predicting complex systems one typically relies on differential equation 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. We show that this can be used to predict paradigmatic, high-dimensional chaotic partial differential equations even when only short and incomplete datasets are available. The forecast horizon for these high dimensional systems is about an order of magnitude larger than the length of the training data.

Original languageEnglish
Article number043005
JournalNew Journal of Physics
Issue number4
StatePublished - Apr 2021
Externally publishedYes


  • complex systems
  • hybrid model
  • machine learning
  • nonlinear dynamics
  • partial differential equations
  • prediction


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