64 citations · 126 across the 15 of their papers we have counts for
3 papers · 1 filter
Graph-based Prior and Forward Models for Inverse Problems on Manifolds with Boundaries
John Harlim, Shixiao Jiang, Hwanwoo Kim +1
This paper develops manifold learning techniques for the numerical solution of PDE-constrained Bayesian inverse problems on manifolds with boundaries. We introduce graphical Matérn…
Solving PDEs on Unknown Manifolds with Machine Learning
Senwei Liang, Shixiao W. Jiang, John Harlim +1
This paper proposes a mesh-free computational framework and machine learning theory for solving elliptic PDEs on unknown manifolds, identified with point clouds, based on diffusion…
Kernel-based methods for Solving Time-Dependent Advection-Diffusion Equations on Manifolds
Qile Yan, Shixiao Willing Jiang, John Harlim
In this paper, we extend the class of kernel methods, the so-called diffusion maps (DM) and ghost point diffusion maps (GPDM), to solve the time-dependent advection-diffusion PDE o…