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arXiv · 2306.05224

Autoencoding for the 'Good Dictionary' of eigen pairs of the Koopman Operator

Neranjaka Jayarathne·Erik M. Bollt
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Abstract

Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through Koopman operator analysis. However, computing Koopman eigen pairs for high-dimensional observable data can be inefficient. This paper proposes using deep autoencoders, a type of deep learning technique, to perform non-linear geometric transformations on raw data before computing Koopman eigen vectors. The encoded data produced by the deep autoencoder is diffeomorphic to a manifold of the dynamical system, and has a significantly lower dimension than the raw data. To handle high-dimensional time series data, Takens's time delay embedding is presented as a pre-processing technique. The paper concludes by presenting examples of these techniques in action.

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Neranjaka Jayarathne, Erik M. Bollt. 2023-06-08. Autoencoding for the 'Good Dictionary' of eigen pairs of the Koopman Operator. https://arxiv.org/abs/2306.05224

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