no code implementations • 5 Oct 2023 • Yifan Chen, Daniel Zhengyu Huang, Jiaoyang Huang, Sebastian Reich, Andrew M Stuart
Our third contribution is to study, and develop efficient algorithms based on Gaussian approximations of the gradient flows; this leads to an alternative to particle methods.
no code implementations • 8 May 2023 • Pau Batlle, Yifan Chen, Bamdad Hosseini, Houman Owhadi, Andrew M Stuart
We introduce a priori Sobolev-space error estimates for the solution of nonlinear, and possibly parametric, PDEs using Gaussian process and kernel based methods.
2 code implementations • 24 Mar 2021 • Yifan Chen, Bamdad Hosseini, Houman Owhadi, Andrew M Stuart
The main idea of our method is to approximate the solution of a given PDE as the maximum a posteriori (MAP) estimator of a Gaussian process conditioned on solving the PDE at a finite number of collocation points.