Error analysis of kernel/GP methods for nonlinear and parametric PDEs

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Pau Batlle, Yifan Chen, Bamdad Hosseini, Houman Owhadi, Andrew M. Stuart

Published: 01 Jan 2025, Last Modified: 06 Nov 2025J. Comput. Phys. 2025EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Highlights•Extension of kernel PDE solvers to parametric PDEs.•Quantitative a priori convergence rates for kernel PDE solvers.•Proof technique is elegant and can be extended to Neural Net solvers.•Numerical experiments demonstrate the sharpness of rates and extend theory.