Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equations

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 Koopman operator associated with nonlinear phenomena, have been rapidly developing by incorporating machine learning methods. Neural ordinary differential equations (NODEs), are a neural network equipped continuum of layers, high parameter memory efficiencies, proposed. In this paper, we propose an algorithm to perform EDMD NODEs. NODEs used find parameter-efficient dictionary provides good finite-dimensional approximation operator. We show superiority efficiency proposed through numerical experiments.