Koopman-Equivariant Gaussian Processes

Petar Bevanda, Max Beier, Alexandre Capone, Stefan Georg Sosnowski, Sandra Hirche, Armin Lederer

TL;DR: We propose time-linear & space-nonlinear Gaussian process models with enhanced generalization that scale to large scale datasets.

Abstract:

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 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.

Submission Number: 1132