Koopman representations aim to learn features of nonlinear dynamical systems (NLDS) which lead to linear dynamics in the latent space. Theoretically, such features can be used to simplify many problems in modeling and control of NLDS. In this work we study autoencoder formulations of this problem, and different ways they can be used to model dynamics, specifically for future state prediction over long horizons. We discover several limitations of predicting future states in the latent space and propose an inference-time mechanism, which we refer to as Periodic Reencoding, for faithfully capturing long term dynamics. We justify this method both analytically and empirically via experiments in low and high dimensional NLDS.

翻译：库普曼表示旨在学习非线性动力系统（NLDS）的特征，这些特征可在潜在空间中实现线性动力学。理论上，此类特征可用于简化NLDS建模与控制中的诸多问题。本文研究了该问题的自编码器形式，以及它们建模动力学的不同方式，特别是长时域未来状态预测。我们发现，在潜在空间中预测未来状态存在若干局限性，并提出一种推理时机制——周期重编码——以忠实地捕捉长期动力学。我们通过低维和高维NLDS实验，从分析和实证两方面验证了该方法的有效性。