Parameter Estimation with Data-Driven Nonparametric Likelihood Functions. - Shixiao W. Jiang; John Harlim (Entropy, 2019)

Ghost Point Diffusion Maps for solving elliptic PDE's on Manifolds with Classical Boundary Conditions. - Shixiao W. Jiang; John Harlim (CoRR, 2020)

Solving PDEs on Unknown Manifolds with Machine Learning. - Senwei Liang; Shixiao W. Jiang; John Harlim; Haizhao Yang (CoRR, 2021)

Graph-based Prior and Forward Models for Inverse Problems on Manifolds with Boundaries. - John Harlim; Shixiao W. Jiang; Hwanwoo Kim; Daniel Sanz-Alonso (CoRR, 2021)

Machine learning for prediction with missing dynamics. - John Harlim; Shixiao W. Jiang; Senwei Liang; Haizhao Yang (J. Comput. Phys., 2021)

Spectral methods for solving elliptic PDEs on unknown manifolds. - Qile Yan; Shixiao Willing Jiang; John Harlim (J. Comput. Phys., 2023)

Radial Basis Approximation of Tensor Fields on Manifolds: From Operator Estimation to Manifold Learning. - John Harlim; Shixiao Willing Jiang; John Wilson Peoples (J. Mach. Learn. Res., 2023)

Kernel-Based Methods for Solving Time-Dependent Advection-Diffusion Equations on Manifolds. - Qile Yan; Shixiao W. Jiang; John Harlim (J. Sci. Comput., 2023)

Generalized Moving Least-Squares for Solving Vector-valued PDEs on Unknown Manifolds. - Rongji Li; Qile Yan; Shixiao W. Jiang (CoRR, 2024)

Generalized finite difference method on unknown manifolds. - Shixiao Willing Jiang; Rongji Li; Qile Yan; John Harlim (J. Comput. Phys., 2024)