Koopman-Equivariant Gaussian Processes
This work addresses the problem of reliable decision-making in dynamical systems, which is crucial for various fields that rely on forecasting and representation learning, such as control systems or time-series analysis, with an incremental approach.
The authors tackled the problem of forecasting and representation learning of dynamical systems, achieving on-par or better performance compared to kernel-based methods with their proposed Koopman-Equivariant Gaussian Processes. Their approach enabled tractable quantification of forecasting and representational uncertainty.
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.