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
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 perturbationsInformation Integration, Organization, and Numerical Harmonic Analysis
Coifman R, Talmon R, Gavish M, Haddad A. Information Integration, Organization, and Numerical Harmonic Analysis. 2015, 254-271. DOI: 10.1002/9781118853887.ch10.Peer-Reviewed Original ResearchPartial differential equationsHarmonic analysisLocal linear modelsLocal similarity modelNumerical harmonic analysisDifferential equationsMathematical frameworkNewtonian calculusGlobal solutionClassical toolsFunctional regressionLinear modelData matrixUnrelated approachesMathematicsSignal processingNumericsEquationsMachine learningGraphGlobal configurationCalculusData analysisGeometryModel
2006
Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
Nadler B, Lafon S, Coifman R, Kevrekidis I. Diffusion maps, spectral clustering and reaction coordinates of dynamical systems. Applied And Computational Harmonic Analysis 2006, 21: 113-127. DOI: 10.1016/j.acha.2005.07.004.Peer-Reviewed Original ResearchFokker-Planck operatorDynamical systemsDifferential operatorsHigh-dimensional stochastic systemsRandom walkProbability distributionDimensional stochastic systemsStochastic differential equationsCorresponding differential operatorComplex dynamical systemsTime evolutionLong-time asymptoticsLow-dimensional Euclidean spaceGeneral probability distributionNormalized graph LaplacianLaplace-Beltrami operatorDimensional Euclidean spaceDiffusion mapsLong-time evolutionSpectral clusteringStochastic systemsDifferential equationsHigh-dimensional dataSlow variablesLarge-scale simulations
1998
Multiscale Inversion of Elliptic Operators
Averbuch A, Beylkin G, Coifman R, Israeli M. Multiscale Inversion of Elliptic Operators. Wavelet Analysis And Its Applications 1998, 7: 341-359. DOI: 10.1016/s1874-608x(98)80013-7.Peer-Reviewed Original ResearchLinear systemsCondition numberElliptic partial differential equationsPartial differential equationsLarge condition numberBoundary conditionsConjugate gradient iterationNumber of iterationsFast adaptive algorithmNumber of operationsDifferential equationsWavelet coordinatesSuch equationsMultiscale inversionDifferential operatorsElliptic operatorsDiagonal preconditionerComplicated equationsPeriodic boundary conditionsGradient iterationPoisson equationGradient algorithmConjugate directionsEquationsAdaptive algorithm
1989
Linear spectral problems, non-linear equations and the δ-method
Beals R, Coifman R. Linear spectral problems, non-linear equations and the δ-method. Inverse Problems 1989, 5: 87. DOI: 10.1088/0266-5611/5/2/002.Peer-Reviewed Original Research
1986
The D-bar approach to inverse scattering and nonlinear evolutions
Beals R, Coifman R. The D-bar approach to inverse scattering and nonlinear evolutions. Physica D Nonlinear Phenomena 1986, 18: 242-249. DOI: 10.1016/0167-2789(86)90184-3.Peer-Reviewed Original ResearchSelf-dual Yang-Mills equationsComplex differential equationsYang-Mills equationsInverse scattering methodDavey–StewartsonDifferential equationsNonlinear equationsSchrödinger equationAssociated hierarchyInverse scatteringNonlinear evolutionEquationsMultidimensional problemsScattering methodInversionProblemR3Scattering