2025
From clutter to clarity: Emergent neural operators via questionnaire metrics
Georgiou A, Manoj A, Su P, Coifman R, Kevrekidis I, Goswami S. From clutter to clarity: Emergent neural operators via questionnaire metrics. Computers & Chemical Engineering 2025, 201: 109201. DOI: 10.1016/j.compchemeng.2025.109201.Peer-Reviewed Original ResearchAdvanced deep learning architecturesReal-world datasetsDeep learning architectureAgent-based systemsSupervised learning modelsAdvection-diffusion partial differential equationLearning architectureScrambled dataLearning techniquesData-driven system identificationNeural operationsEfficient emulationGenerative modelLearning modelsParameter embeddingDatasetFramework’s potentialSystem identificationClutter dataSystem dynamicsDifferential equationsFrameworkPartial differential equationsEmbeddingArchitectureFrom disorganized data to emergent dynamic models: Questionnaires to partial differential equations
Sroczynski D, Kemeth F, Georgiou A, Coifman R, Kevrekidis I. From disorganized data to emergent dynamic models: Questionnaires to partial differential equations. PNAS Nexus 2025, 4: pgaf018. PMID: 39898180, PMCID: PMC11786195, DOI: 10.1093/pnasnexus/pgaf018.Peer-Reviewed Original ResearchComplex dynamical network modelData-driven derivationData-driven wayDisorganized dataMachine learningPartial differential equationsNetwork modelType of dataEvolutionary partial differential equationsDiffusion mapsDynamic network modelEvolution equationsEmbedded geometryEvolving systemSymmetry breakingTensor typeDifferential equationsTranslational invarianceDerivation of parametersPDE modelAdvection-diffusion modelSmooth parametrization
2015
Information 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
2004
Correcting Nonuniformities in MRI Intensities Using Entropy Minimization Based on an Elastic Model
Bansal R, Staib L, Peterson B. Correcting Nonuniformities in MRI Intensities Using Entropy Minimization Based on an Elastic Model. Lecture Notes In Computer Science 2004, 3216: 78-86. DOI: 10.1007/978-3-540-30135-6_10.Peer-Reviewed Original ResearchPartial differential equationsConstraints of interestEntropy minimizationBody forceBias fieldDifferential equationsObserved imagesMathematical formulationOverall entropyElastic deformationEntropyElastic modelHomogeneous regionsMinimizationFieldConstraintsFormulationEquationsNonuniformityMultiplicative bias fieldAlgorithmOriginal imageDeformationForce
1999
Recovery of Soft Tissue Object Deformation from 3D Image Sequences Using Biomechanical Models
Papademetris X, Shi P, Dione D, Sinusas A, Todd Constable R, Duncan J. Recovery of Soft Tissue Object Deformation from 3D Image Sequences Using Biomechanical Models. Lecture Notes In Computer Science 1999, 1613: 352-357. DOI: 10.1007/3-540-48714-x_28.Peer-Reviewed Original Research
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
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