Koopman Learning with Episodic Memory
This addresses a specific bottleneck in Koopman learning for dynamical systems, offering incremental improvements in prediction accuracy.
The paper tackles the problem of Koopman learning lacking the ability to leverage its own failures by equipping it with an episodic memory mechanism for global recall of similar past dynamics, resulting in significant improvements in prediction on synthetic and real-world data.
Koopman operator theory has found significant success in learning models of complex, real-world dynamical systems, enabling prediction and control. The greater interpretability and lower computational costs of these models, compared to traditional machine learning methodologies, make Koopman learning an especially appealing approach. Despite this, little work has been performed on endowing Koopman learning with the ability to leverage its own failures. To address this, we equip Koopman methods -- developed for predicting non-autonomous time-series -- with an episodic memory mechanism, enabling global recall of (or attention to) periods in time where similar dynamics previously occurred. We find that a basic implementation of Koopman learning with episodic memory leads to significant improvements in prediction on synthetic and real-world data. Our framework has considerable potential for expansion, allowing for future advances, and opens exciting new directions for Koopman learning.