Humboldt-Universität zu Berlin - Mathematisch-Naturwissen­schaft­liche Fakultät - International Research Training Group 1740

Seminar Talk - M. Gelbrecht

  • Wann 06.10.2020 von 13:00 bis 14:00
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Seminar Talk



Maximilian Gelbrecht Potsdam-Institute for Climate Impact Research, Project C1)

Title: The Neural Partial Differential Equations for Chaotic Systems

Abstract: When predicting complex systems one typically relies on models in the form of differential equation. Often through the modeling process these differential equations can be incomplete, missing unknown influences or higher order effects. Data-driven methods can fill these gaps. Recent ad- vances like the universal differential equations framework enable us compose differential equation with universal function approximators such as artifical neural networks as part of the equation. We demonstrate that this approach can be used to make prediction of chaotic partial differential equations like the Complex Ginsburg Landau equations and the Kuramoto Sivashinsky equations even when only short and incomplete datasets to train the artificial neural network are available. The forecast horizon for these high dimensional systems exceeds the length of the training set by far as it is about an order of magnitude larger than the length of the training data.

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