Course Correcting Koopman Representations

• URL: http://arxiv.org/abs/2310.15386v2
• Date: Thu, 23 Nov 2023 06:32:10 GMT
• Title: Course Correcting Koopman Representations
• Authors: Mahan Fathi and Clement Gehring and Jonathan Pilault and David Kanaa and Pierre-Luc Bacon and Ross Goroshin
• Abstract summary: We study autoencoder formulations of this problem, and different ways they can be used to model dynamics. We propose an inference-time mechanism, which we refer to as Periodic Reencoding, for faithfully capturing long term dynamics.
• Score: 12.517740162118855
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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