Detecting Intrinsic Slow Variables in Stochastic Dynamical Systems by Anisotropic Diffusion maps

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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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2009
Accession Number
ADA552145

Entities

People

  • Amit Singer
  • Radek Erban
  • Ronald R. Coifman
  • Yannís G. Kevrekidis

Organizations

  • Princeton University

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Chemical Reactions
  • Data Analysis
  • Data Sets
  • Differential Equations
  • Diffusion
  • Dimensionality Reduction
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Factor Analysis
  • Information Processing
  • Information Science
  • Mathematics
  • New York
  • Point Clouds
  • Stochastic Processes

Readers

  • Combustion science or combustion engineering.
  • Neural Network Machine Learning.
  • Statistical inference.