Machine learning enhanced Hankel dynamic-mode decomposition
Abstract
While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a merging of machine learning tools with what is called the dynamic-mode decomposition (DMD). This general approach has been shown to be an especially promising avenue for accurate model development. Building on this prior body of work, we develop a deep learning DMD based method, which makes use of the fundamental insight of Takens’ embedding theorem to build an adaptive learning scheme that better approximates higher dimensional and chaotic dynamics. We call this method the Deep Learning Hankel DMD. We likewise explore how our method learns mappings, which tend, after successful training, to significantly change the mutual information between dimensions in the dynamics. This appears to be a key feature in enhancing DMD overall, and it should help provide further insight into developing other deep learning methods for time series analysis and model generation.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 01, 2023
- Source ID
- 10.1063/5.0150689
Entities
People
- Andrew Tuma
- Christopher W. Curtis
- Daniel Jay Alford-Lago
- Erik Bollt
Organizations
- Air Force Office of Scientific Research
- Army Research Office
- Clarkson University
- National Institutes of Health
- Naval Information Warfare Center Pacific
- Office of Naval Research
- San Diego State University