2024
Learning integral operators via neural integral equations
Zappala E, Fonseca A, Caro J, Moberly A, Higley M, Cardin J, Dijk D. Learning integral operators via neural integral equations. Nature Machine Intelligence 2024, 6: 1046-1062. DOI: 10.1038/s42256-024-00886-8.Peer-Reviewed Original ResearchSelf-attentionNon-local operatorsMachine learningModeling complex systemsReal-world dataHigher-dimensional problemsComplex systemsDynamic embeddingsIntegral equationsModel capacitySpatiotemporal dependenciesIntegral operatorsSecond-kind integral equationsIntegral equation solversModeling capabilitiesNonlinear operatorsTheoretical analysisNon-local systemNumerical benchmarksMachineLearningApproximate resultsNavier-StokesEquation solverScalability
2023
Neural Integro-Differential Equations
Zappala E, de O. Fonseca A, Moberly A, Higley M, Abdallah C, Cardin J, Van Dijk D. Neural Integro-Differential Equations. Proceedings Of The AAAI Conference On Artificial Intelligence 2023, 37: 11104-11112. DOI: 10.1609/aaai.v37i9.26315.Peer-Reviewed Original ResearchIntegro-differential equationsIntegral operatorsDifferential equationsContinuous dynamical systemsNon-local dynamicsDynamical systemsInitial conditionsEquationsNeural networkTime extrapolationOperatorsIntegralsFundamental problemSuch dynamicsLatent spaceDynamicsNon-local processesBrain activity recordingsBrain dynamicsData scienceDifferential componentsIntegrandGeneralizationTheoryNetwork