Speaker: Dr. Chris Vales, Dartmouth
Title: "Accelerated kernel methods for spatiotemporal dynamics"
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 demonstrate the extraction of patterns from the modified Hasegawa-Wakatani equations of plasma dynamics, and conclude with an application to data driven dynamical closure for the shallow water equations.
Bio: Chris Vales is a research postdoc in the Mathematics department at Dartmouth College. His current work is focused on topics related to dynamical closure, data assimilation and pattern extraction for spatiotemporal dynamics, employing data driven kernel methods and the statistical description of deterministic dynamics.
In person attendance at this seminar is only open to Columbia University affiliates. External guests are welcome to attend remotely. Please contact [email protected] if you need the Zoom link for this seminar.