109 citations · 443 across the 45 of their papers we have counts for
4 papers · 1 filter
Iterated Diffusion Maps for Feature Identification
Tyrus Berry, John Harlim
Recently, the theory of diffusion maps was extended to a large class of local kernels with exponential decay which were shown to represent various Riemannian geometries on a data s…
Semiparametric forecasting and filtering: correcting low-dimensional model error in parametric models
Tyrus Berry, John Harlim
Semiparametric forecasting and filtering are introduced as a method of addressing model errors arising from unresolved physical phenomena. While traditional parametric models are a…
Parametric Reduced Models for the Nonlinear Schrödinger Equation
John Harlim, Xiantao Li
Reduced models for the (defocusing) nonlinear Schrödinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy obs…
Forecasting Turbulent Modes with Nonparametric Diffusion Models: Learning from noisy data
Tyrus Berry, John Harlim
In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical system…