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Abstract:
When predicting complex systems one typically relies on differential equation which can often be
incomplete, missing unknown infl
uences 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.
