2015
Intrinsic modeling of stochastic dynamical systems using empirical geometry
Talmon R, Coifman R. Intrinsic modeling of stochastic dynamical systems using empirical geometry. Applied And Computational Harmonic Analysis 2015, 39: 138-160. DOI: 10.1016/j.acha.2014.08.006.Peer-Reviewed Original ResearchLow-dimensional manifoldDynamical systemsEmpirical geometryReal-world dynamical systemsStochastic dynamical systemsNon-Gaussian tracking problemsNonlinear filtering applicationsNonlinear differential equationsIntrinsic Riemannian metricMarkov chain schemeEmpirical probability densityLocal tangent spaceIntrinsic modelDifferential equationsIntrinsic modelingKnowledge of modelsTangent spaceProbability densityMathematical calibrationTracking problemInverse problemRiemannian metricLaplace operatorRandom measurementsSmall perturbations
2009
Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps
Singer A, Erban R, Kevrekidis IG, Coifman RR. Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps. Proceedings Of The National Academy Of Sciences Of The United States Of America 2009, 106: 16090-16095. PMID: 19706457, PMCID: PMC2752552, DOI: 10.1073/pnas.0905547106.Peer-Reviewed Original ResearchConceptsStochastic dynamical systemsModel reduction approachHigh dimensional dynamic dataDynamical systemsNonlinear independent component analysisLocal principal component analysisSlow variablesMarkov matrixGood observablesDiffusion mapsNetwork simulationAnisotropic diffusionReduction approachData analysis techniqueAnalysis techniquesEigenvectorsDynamic dataObservablesIndependent component analysisComponent analysisSimulationsMatrix