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

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

doi:10.1073/pnas.0905547106

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

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

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117 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 language	English (US)
Pages (from-to)	16090-16095
Number of pages	6
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	106
Issue number	38
DOIs	https://doi.org/10.1073/pnas.0905547106
State	Published - Sep 22 2009

All Science Journal Classification (ASJC) codes

General

Keywords

Chemical reactions
Dimensionality reduction
Slow manifold

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10.1073/pnas.0905547106

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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.",

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AU - Erban, Radek

AU - Kevrekidis, Ioannis G.

AU - Coifman, Ronald R.

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AB - 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.

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KW - Dimensionality reduction

KW - Slow manifold

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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