109 citations · 443 across the 45 of their papers we have counts for
3 papers · 1 filter
Kernel-based Prediction of Non-Markovian Time Series
Faheem Gilani, Dimitrios Giannakis, John Harlim
A nonparametric method to predict non-Markovian time series of partially observed dynamics is developed. The prediction problem we consider is a supervised learning task of finding…
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…
Bridging data science and dynamical systems theory
Tyrus Berry, Dimitrios Giannakis, John Harlim
This short review describes mathematical techniques for statistical analysis and prediction in dynamical systems. Two problems are discussed, namely (i) the supervised learning pro…