Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps

Amit Singer, Radek Erban, Ioannis G. Kevrekidis, Ronald R. Coifman

Research output: Contribution to journalArticle

80 Scopus citations

Abstract

Nonlinear independent component analysis is combined with diffusion-map data analysis techniques to detect good observables in high-dimensional dynamic data. These detections are achieved by integrating local principal component analysis of simulation bursts by using eigenvectors of a Markov matrix describing anisotropic diffusion. The widely applicable procedure, a crucial step in model reduction approaches, is illustrated on stochastic chemical reaction network simulations.

Original languageEnglish (US)
Pages (from-to)16090-16095
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume106
Issue number38
DOIs
StatePublished - Sep 22 2009

All Science Journal Classification (ASJC) codes

  • General

Keywords

  • Chemical reactions
  • Dimensionality reduction
  • Slow manifold

Fingerprint Dive into the research topics of 'Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps'. Together they form a unique fingerprint.

  • Cite this