109 citations · 443 across the 45 of their papers we have counts for
4 papers · 1 filter
Fractional Diffusion Maps
Harbir Antil, Tyrus Berry, John Harlim
In this paper, we extend the diffusion maps algorithm on a family of heat kernels that are either local (having exponential decay) or nonlocal (having polynomial decay), arising in…
Approximating solutions of linear elliptic PDE's on a smooth manifold using local kernels
Faheem Gilani, John Harlim
A mesh-free numerical method for solving linear elliptic PDE's using the local kernel theory that was developed for manifold learning is proposed. In particular, this novel approac…
Parameter estimation with data-driven nonparametric likelihood functions
Shixiao W. Jiang, John Harlim
In this paper, we consider a surrogate modeling approach using a data-driven nonparametric likelihood function constructed on a manifold on which the data lie (or to which they are…
Data-Driven Computational Methods: Parameter and Operator Estimations (Chapter 1)
John Harlim
Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-p…