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Self-Consistent Velocity Matching of Probability Flows

hal.structure.identifierMIT Computer Science & Artificial Intelligence Lab [MIT CSAIL]
dc.contributor.authorLI, Lingxiao
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorHURAULT, Samuel
hal.structure.identifierMIT Computer Science & Artificial Intelligence Lab [MIT CSAIL]
dc.contributor.authorSOLOMON, Justin
dc.date.accessioned2024-04-04T02:31:15Z
dc.date.available2024-04-04T02:31:15Z
dc.date.conference2023-12-10
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190292
dc.description.abstractEnWe present a discretization-free scalable framework for solving a large class of mass-conserving partial differential equations (PDEs), including the time-dependent Fokker-Planck equation and the Wasserstein gradient flow. The main observation is that the time-varying velocity field of the PDE solution needs to be self-consistent: it must satisfy a fixed-point equation involving the probability flow characterized by the same velocity field. Instead of directly minimizing the residual of the fixed-point equation with neural parameterization, we use an iterative formulation with a biased gradient estimator that bypasses significant computational obstacles with strong empirical performance. Compared to existing approaches, our method does not suffer from temporal or spatial discretization, covers a wider range of PDEs, and scales to high dimensions. Experimentally, our method recovers analytical solutions accurately when they are available and achieves superior performance in high dimensions with less training time compared to alternatives.
dc.description.sponsorshipRepenser la post-production d'archives avec des méthodes à patch, variationnelles et par apprentissage - ANR-19-CE23-0027
dc.language.isoen
dc.title.enSelf-Consistent Velocity Matching of Probability Flows
dc.typeCommunication dans un congrès
dc.subject.halInformatique [cs]/Intelligence artificielle [cs.AI]
dc.identifier.arxiv2301.13737
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleNeural Information Processing Systems (NeurIPS'23)
bordeaux.countryUS
bordeaux.conference.cityLa Nouvelle-Orléans, Louisiane
bordeaux.peerReviewedoui
hal.identifierhal-04399169
hal.version1
hal.invitednon
hal.proceedingsoui
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04399169v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=LI,%20Lingxiao&HURAULT,%20Samuel&SOLOMON,%20Justin&rft.genre=unknown


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