MetaLearning for Koopman Spectral Analysis with Short Timeseries
Abstract
Koopman spectral analysis has attracted attention for nonlinear dynamical systems since we can analyze nonlinear dynamics with a linear regime by embedding data into a Koopman space by a nonlinear function. For the analysis, we need to find appropriate embedding functions. Although several neural networkbased methods have been proposed for learning embedding functions, existing methods require long timeseries for training neural networks. This limitation prohibits performing Koopman spectral analysis in applications where only short timeseries are available. In this paper, we propose a metalearning method for estimating embedding functions from unseen short timeseries by exploiting knowledge learned from related but different timeseries. With the proposed method, a representation of a given short timeseries is obtained by a bidirectional LSTM for extracting its properties. The embedding function of the short timeseries is modeled by a neural network that depends on the timeseries representation. By sharing the LSTM and neural networks across multiple timeseries, we can learn common knowledge from different timeseries while modeling timeseriesspecific embedding functions with the timeseries representation. Our model is trained such that the expected test prediction error is minimized with the episodic training framework. We experimentally demonstrate that the proposed method achieves better performance in terms of eigenvalue estimation and future prediction than existing methods.
 Publication:

arXiv eprints
 Pub Date:
 February 2021
 arXiv:
 arXiv:2102.04683
 Bibcode:
 2021arXiv210204683I
 Keywords:

 Statistics  Machine Learning;
 Computer Science  Machine Learning;
 Mathematics  Dynamical Systems