@article{Jayarathne2024, 
author = {Neranjaka Jayarathne and Erik M. Bollt},
title = {Autoencoding for the "Good Dictionary" of eigenpairs of the Koopman operator},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {998-1022},
keywords = {deep learning, autoencoders, data driven science, reduced order modelling, Koopman analysis},
url = {https://www.sciopen.com/article/10.3934/math.2024050},
doi = {10.3934/math.2024050},
abstract = {Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through the Koopman operator(KO) analysis. However, computing Koopman eigenpairs for high-dimensional observable data can be inefficient. This paper proposes using deep autoencoders(AE), a type of deep learning technique, to perform nonlinear geometric transformations on raw data before computing Koopman eigenvectors. The encoded data produced by the deep AE 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' time delay embedding is presented as a preprocessing technique. The paper concludes by presenting examples of these techniques in action.}
}