Group-Convolutional Extended Dynamic Mode Decomposition

Understand

This paper explores the integration of symmetries into the Koopman-operator framework for the analysis and efficient learning of equivariant dynamical systems using a group-convolutional approach.

• Approximating the Koopman operator by finite-dimensional surrogates, e.g., via extended dynamic mode decomposition (EDMD), is challenging for high-dimensional systems due to computational constraints.
• To tackle this problem with a particular focus on EDMD, we demonstrate -- under suitable equivarance assumptions on the system and the observables -- that the optimal EDMD matrix is equivariant.
• That is, its action on states can be described by group convolutions and the generalized Fourier transform.