CSE Community Seminar | October 23, 2026

Abstract

We consider the use of kernel methods for the extraction of spatiotemporal patterns from PDE simulation data, focusing on spatiotemporal correlation kernels that act on the product space of temporal snapshots and spatial gridpoints. The employed family of kernels leads to kernel eigenfunctions that are invariant under the spatial symmetries of the dynamics and inherently spatiotemporal, enabling each eigenfunction to encode a complex and dynamically relevant pattern. Specific attention is paid to the scalable implementation of the method via low rank approximation and distributed GPU computing. We conclude with the extraction of patterns from the modified Hasegawa-Wakatani equations of plasma dynamics, and with an application to data driven dynamical closure for the shallow water equations.