Deep learning enhanced dynamic mode decomposition
Abstract
Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of this infinite-dimensional operator can be difficult. The extended dynamic mode decomposition (EDMD) is one such method for generating approximations to Koopman spectra and modes, but the EDMD method faces its own set of challenges due to the need of user defined observables. To address this issue, we explore the use of autoencoder networks to simultaneously find optimal families of observables, which also generate both accurate embeddings of the flow into a space of observables and submersions of the observables back into flow coordinates. This network results in a global transformation of the flow and affords future state prediction via the EDMD and the decoder network. We call this method the deep learning dynamic mode decomposition (DLDMD). The method is tested on canonical nonlinear data sets and is shown to produce results that outperform a standard DMD approach and enable data-driven prediction where the standard DMD fails.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 01, 2022
- Source ID
- 10.1063/5.0073893
Entities
People
- Alexander Thomas Ihler
- Christopher W. Curtis
- Daniel Jay Alford-Lago
- Opal Issan
Organizations
- Naval Information Warfare Center Pacific
- Office of Naval Research
- San Diego State University
- University of California, Irvine
- University of California, San Diego