Learning Linear Embeddings for Non-Linear Network Dynamics with Koopman Message Passing

• URL: http://arxiv.org/abs/2305.09060v1
• Date: Mon, 15 May 2023 23:00:25 GMT
• Title: Learning Linear Embeddings for Non-Linear Network Dynamics with Koopman Message Passing
• Authors: King Fai Yeh, Paris Flood, William Redman, and Pietro Li\`o
• Abstract summary: We present a novel approach based on Koopman operator theory and message passing networks. We find a linear representation for the dynamical system which is globally valid at any time step. The linearisations found by our method produce predictions on a suite of network dynamics problems that are several orders of magnitude better than current state-of-the-art techniques.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep learning approaches, perform poorly on non-linear network dynamics problems as they do not address the underlying geometric structure. In this paper we present a novel approach based on Koopman operator theory and message passing networks that finds a linear representation for the dynamical system which is globally valid at any time step. The linearisations found by our method produce predictions on a suite of network dynamics problems that are several orders of magnitude better than current state-of-the-art techniques. We also apply our approach to the highly non-linear training dynamics of neural network architectures, and obtain linear representations which can generate network parameters with comparable performance to networks trained by classical optimisers.

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