  Koopman operator theory, a data-driven dynamical systems framework, has found
significant success in learning models from complex, real-world data sets,
enabling state-of-the-art 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 learn from its own mistakes. To address this, we equip Koopman
methods - developed for predicting non-stationary 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.
