109 citations · 443 across the 45 of their papers we have counts for
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math.NA2022★ 8 cited
Spectral methods for solving elliptic PDEs on unknown manifolds
Qile Yan, Shixiao Jiang, John Harlim
In this paper, we propose a mesh-free numerical method for solving elliptic PDEs on unknown manifolds, identified with randomly sampled point cloud data. The PDE solver is formulat…
physics.data-an2022★ 10 cited
A Data-Driven Statistical-Stochastic Surrogate Modeling Strategy for Complex Nonlinear Non-stationary Dynamics
Di Qi, John Harlim
We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing pe…
math.NA2022★ 4 cited
Radial basis approximation of tensor fields on manifolds: From operator estimation to manifold learning
John Harlim, Shixiao Willing Jiang, John Wilson Peoples
In this paper, we study the Radial Basis Function (RBF) approximation to differential operators on smooth tensor fields defined on closed Riemannian submanifolds of Euclidean space…