2017
Reconstruction of normal forms by learning informed observation geometries from data
Yair O, Talmon R, Coifman RR, Kevrekidis IG. Reconstruction of normal forms by learning informed observation geometries from data. Proceedings Of The National Academy Of Sciences Of The United States Of America 2017, 114: e7865-e7874. PMID: 28831006, PMCID: PMC5617245, DOI: 10.1073/pnas.1620045114.Peer-Reviewed Original ResearchNormal formNonlinear differential equationsDynamical systems theoryAppropriate normal formFundamental physical quantitiesDifferential equationsDynamical regimesState variablesPhysical quantitiesPhysical lawsSystems theoryGeometry learningEmpirical observationsObservation geometryHeart of scienceDynamicsPrior knowledgeEquationsRealizationLawParametersGeometryTheoryExplicit referenceForm
2014
Diffusion maps for changing data
Coifman R, Hirn M. Diffusion maps for changing data. Applied And Computational Harmonic Analysis 2014, 36: 79-107. DOI: 10.1016/j.acha.2013.03.001.Peer-Reviewed Original ResearchParameter spaceDiffusion mapsHigh-dimensional dataLow-dimensional spaceApproximation theoremGraph LaplacianIntrinsic geometryDimensional spaceSet of parametersNonlinear mappingDimensional dataGlobal behaviorEmbedding changesSpaceTypes of dataTheoremPowerful toolLaplacianGraphGeometryTermsEmbeddingDistanceParameters