Publication:
Hybrid PDE solver for data-driven problems and modern branching

dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.contributor.authorBernal Martínez, Francisco Manuel
dc.contributor.authorDos Reis, Gonçalo
dc.contributor.authorSmith, Greig
dc.date.accessioned2021-03-10T11:16:09Z
dc.date.available2021-03-10T11:16:09Z
dc.date.issued2017-12
dc.description.abstractThe numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations about the parallelization and scalability of realistic problems are often critical enough to warrant acknowledgement in the modelling phase. The purpose of this paper is to spread awareness of the Probabilistic Domain Decomposition (PDD) method, a fresh approach to the parallelization of PDEs with excellent scalability properties. The idea exploits the stochastic representation of the PDE and its approximation via Monte Carlo in combination with deterministic high-performance PDE solvers. We describe the ingredients of PDD and its applicability in the scope of data science. In particular, we highlight recent advances in stochastic representations for non-linear PDEs using branching diffusions, which have significantly broadened the scope of PDD. We envision this work as a dictionary giving large-scale PDE practitioners references on the very latest algorithms and techniques of a non-standard, yet highly parallelizable, methodology at the interface of deterministic and probabilistic numerical methods. We close this work with an invitation to the fully non-linear case and open research questions.en
dc.format.extent24
dc.identifier.bibliographicCitationBERNAL, F., DOS REIS, G., SMITH, G. (2017). Hybrid PDE solver for data-driven problems and modern branching. European Journal of Applied Mathematics, 28(6), 949–972.en
dc.identifier.doihttps://doi.org/10.1017/S0956792517000109
dc.identifier.issn0956-7925
dc.identifier.publicationfirstpage949
dc.identifier.publicationissue6
dc.identifier.publicationlastpage972
dc.identifier.publicationtitleEuropean Journal of Applied Mathematicsen
dc.identifier.publicationvolume28
dc.identifier.urihttps://hdl.handle.net/10016/32093
dc.identifier.uxxiAR/0000026511
dc.language.isoeng
dc.publisherCambridge University Pressen
dc.rights© Cambridge University Press 2017en
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accesses
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherProbabilistic domain decompositionen
dc.subject.otherHigh-performance parallel computingen
dc.subject.otherMarked branching diffusionsen
dc.subject.otherHybrid non-Linear PDE solversen
dc.subject.otherMonte carlo methodsen
dc.subject.otherPrimary: 65C05en
dc.subject.other65C30
dc.subject.otherSecondary: 65N55en
dc.subject.other60H35
dc.subject.other91-XX
dc.subject.other35CXX
dc.titleHybrid PDE solver for data-driven problems and modern branchingen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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