Mori-Zwanzig latent space Koopman closure for nonlinear autoencoder

arXiv:2310.10745v2 Announce Type: replace
Abstract: The Koopman operator presents an attractive approach to achieve global linearization of nonlinear systems, making it a valuable method for simplifying the understanding of complex dynamics. While data-driven methodologies have exhibited promise in approximating finite Koopman operators, they grapple with various challenges, such as the judicious selection of observables, dimensionality reduction, and the ability to predict complex system behaviors accurately. This study presents a novel approach termed Mori-Zwanzig autoencoder (MZ-AE) to robustly approximate the Koopman …

abstract arxiv autoencoder challenges cs.lg data data-driven dynamics global linearization making math.ds operators physics.flu-dyn simplifying space stat.ml systems type understanding