2023
Neural Integro-Differential Equations
Zappala E, 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
2020
TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics.
Tong A, Huang J, Wolf G, van Dijk D, Krishnaswamy S. TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics. Proceedings Of Machine Learning Research 2020, 119: 9526-9536. PMID: 34337419, PMCID: PMC8320749.Peer-Reviewed Original ResearchOptimal transportNormalizing FlowsOptimal transport networksContinuous dynamicsTarget distributionTransport-based modelContinuous pathPaths of pointsArbitrary pathTransport networkSingle-cell RNA sequencing technologyDynamicsIndividual trajectoriesCellular dynamicsFlowPathDistributionNon-linear pathPairwise matchingPointTrajectoriesDynamic process
2019
Modeling Global Dynamics from Local Snapshots with Deep Generative Neural Networks
Gigante S, van Dijk D, Moon K, Strzalkowski A, Wolf G, Krishnaswamy S. Modeling Global Dynamics from Local Snapshots with Deep Generative Neural Networks. 2019, 00: 1-4. DOI: 10.1109/sampta45681.2019.9030978.Peer-Reviewed Original ResearchStochastic dynamic systemsDeep generative neural networksProbability distributionDynamic systemsMarkov modelGlobal dynamicsLocal snapshotGenerative neural networksKalman filterSnapshot dataNeural networkNeural network frameworkRecurrent neural networkSuch systemsNext stateModeling networkNetwork frameworkDynamicsShallow modelsLocal transitionsHypothetical trajectoryModelBiological systemsNatural sciencesLongitudinal measurements