Koopman-Equivariant Gaussian Processes

• URL: http://arxiv.org/abs/2502.06645v1
• Date: Mon, 10 Feb 2025 16:35:08 GMT
• Title: Koopman-Equivariant Gaussian Processes
• Authors: Petar Bevanda, Max Beier, Armin Lederer, Alexandre Capone, Stefan Sosnowski, Sandra Hirche,
• Abstract summary: We propose a family of Gaussian processes (GP) for dynamical systems with linear time-invariant responses.<n>This linearity allows us to tractably quantify forecasting and representational uncertainty.<n>Experiments demonstrate on-par and often better forecasting performance compared to kernel-based methods for learning dynamical systems.
• Score: 39.34668284375732
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear time-invariant responses, which are nonlinear only in initial conditions. This linearity allows us to tractably quantify forecasting and representational uncertainty, simultaneously alleviating the challenge of computing the distribution of trajectories from a GP-based dynamical system and enabling a new probabilistic treatment of learning Koopman operator representations. Using a trajectory-based equivariance -- which we refer to as \textit{Koopman equivariance} -- we obtain a GP model with enhanced generalization capabilities. To allow for large-scale regression, we equip our framework with variational inference based on suitable inducing points. Experiments demonstrate on-par and often better forecasting performance compared to kernel-based methods for learning dynamical systems.

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