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- ItemAnalysis of a bistable climate toy model with physics-based machine learning methods(Berlin ; Heidelberg : Springer, 2021) Gelbrecht, Maximilian; Lucarini, Valerio; Boers, Niklas; Kurths, JürgenWe propose a comprehensive framework able to address both the predictability of the first and of the second kind for high-dimensional chaotic models. For this purpose, we analyse the properties of a newly introduced multistable climate toy model constructed by coupling the Lorenz ’96 model with a zero-dimensional energy balance model. First, the attractors of the system are identified with Monte Carlo Basin Bifurcation Analysis. Additionally, we are able to detect the Melancholia state separating the two attractors. Then, Neural Ordinary Differential Equations are applied to predict the future state of the system in both of the identified attractors.
- ItemNeural partial differential equations for chaotic systems([London] : IOP, 2021) Gelbrecht, Maximilian; Boers, Niklas; Kurths, JürgenWhen 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.