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math.NA2021★ 3 cited
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…
math.NA2020
Ghost Point Diffusion Maps for solving elliptic PDE's on Manifolds with Classical Boundary Conditions
Shixiao W. Jiang, John Harlim
In this paper, we extend the class of kernel methods, the so-called diffusion maps (DM), and its local kernel variants, to approximate second-order differential operators defined o…
math.NA2019
Machine Learning for Prediction with Missing Dynamics
John Harlim, Shixiao W. Jiang, Senwei Liang +1
This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the pre…