109 citations · 443 across the 45 of their papers we have counts for
8 papers · 1 filter
Spectral Convergence of Symmetrized Graph Laplacian on manifolds with boundary
J. Wilson Peoples, John Harlim
We study the spectral convergence of a symmetrized Graph Laplacian matrix induced by a Gaussian kernel evaluated on pairs of embedded data, sampled from a manifold with boundary, a…
Stationary Density Estimation of Itô Diffusions Using Deep Learning
Yiqi Gu, John Harlim, Senwei Liang +1
In this paper, we consider the density estimation problem associated with the stationary measure of ergodic Itô diffusions from a discrete-time series that approximate the solution…
Machine Learning-Based Statistical Closure Models for Turbulent Dynamical Systems
Di Qi, John Harlim
We propose a Machine Learning (ML) non-Markovian closure modeling framework for accurate predictions of statistical responses of turbulent dynamical systems subjected to external f…
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…