Solving and learning nonlinear PDEs with Gaussian processes

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

Published: 2021, Last Modified: 06 Nov 2025J. Comput. Phys. 2021EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Highlights•A rigorous and unified framework for solving and learning nonlinear PDEs.•The proposed framework is based on techniques derived from Gaussian process regression and kernel methods.•It is provably convergent and inherits complexity vs accuracy guarantees of state of the art dense kernel matrix solvers.•It is interpretable and amenable to numerical analysis.