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.

翻译：库普曼算子理论作为一种数据驱动的动力系统框架，在从复杂真实世界数据集中学习模型方面取得了显著成功，实现了最先进的预测与控制能力。与传统机器学习方法相比，这类模型具有更强的可解释性和更低的计算成本，这使得库普曼学习成为一种极具吸引力的方法。尽管如此，目前鲜有研究赋予库普曼学习方法从自身错误中学习的能力。为解决这一问题，我们为用于预测非平稳时间序列的库普曼方法配备了情景记忆机制，使其能够全局回忆（或关注）先前出现类似动态的时间段。研究发现，基于情景记忆的库普曼学习基本实现能够显著提升合成数据与真实世界数据的预测性能。该框架具有极大的扩展潜力，为未来研究进步奠定基础，并为库普曼学习开辟了令人振奋的新方向。