Machine Learning Enhanced Hankel Dynamic-Mode Decomposition
This work addresses the problem of accurate model development from time series for researchers in dynamical systems and machine learning, but it appears incremental as it builds on prior merging of machine learning with dynamic mode decomposition.
The paper tackles the challenge of developing dynamical models from time series by introducing a deep learning method called Deep Learning Hankel DMD (DLHDMD), which uses Takens' Embedding Theorem to better approximate higher-dimensional and chaotic dynamics, though no concrete numbers are provided for its performance.
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 (DLHDMD). 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 the DMD overall, and it should help provide further insight for developing other deep learning methods for time series analysis and model generation.