Course Correcting Koopman Representations
This work addresses modeling and control challenges in nonlinear dynamical systems, but it is incremental as it builds on existing autoencoder formulations with a specific inference-time fix.
The paper tackled the problem of long-term future state prediction in nonlinear dynamical systems using Koopman representations, discovering limitations in latent space predictions and proposing a Periodic Reencoding mechanism that improved accuracy, as validated through experiments in low and high dimensional systems.
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.