109 citations · 443 across the 45 of their papers we have counts for
5 papers · 1 filter
Estimating linear response statistics using orthogonal polynomials: An RKHS formulation
He Zhang, John Harlim, Xiantao Li
We study the problem of estimating linear response statistics under external perturbations using time series of unperturbed dynamics. Based on the fluctuation-dissipation theory, t…
Kernel Methods for Bayesian Elliptic Inverse Problems on Manifolds
John Harlim, Daniel Sanz-Alonso, Ruiyi Yang
This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Spe…
Linear Response Based Parameter Estimation in the Presence of Model Error
He Zhang, John Harlim, Xiantao Li
Recently, we proposed a method to estimate parameters of stochastic dynamics based on the linear response statistics. The method rests upon a nonlinear least-squares problem that t…
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…
Modeling of Missing Dynamical Systems: Deriving Parametric Models using a Nonparametric Framework
Shixiao W. Jiang, John Harlim
In this paper, we consider modeling missing dynamics with a nonparametric non-Markovian model, constructed using the theory of kernel embedding of conditional distributions on appr…