Nonlinear phenomena can be analyzed via linear techniques using operator-theoretic approaches. Data-driven method called the extended dynamic mode decomposition (EDMD) and its variants, which approximate the Koopman operator associated with the nonlinear phenomena, have been rapidly developing by incorporating machine learning methods. Neural ordinary differential equations (NODEs), which are a neural network equipped with a continuum of layers, and have high parameter and memory efficiencies, have been proposed. In this paper, we propose an algorithm to perform EDMD using NODEs. NODEs are used to find a parameter-efficient dictionary which provides a good finite-dimensional approximation of the Koopman operator. We show the superiority of the parameter efficiency of the proposed method through numerical experiments.
@article{arxiv.2110.01450,
title = {Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equations},
author = {Hiroaki Terao and Sho Shirasaka and Hideyuki Suzuki},
journal= {arXiv preprint arXiv:2110.01450},
year = {2022}
}
Comments
Corrigendum: The loss function in Eq. (20) is not what we have used in our code. Please replace the sum of squared error in Eq. (20) with the mean squared error