Interacting particle solutions of Fokker–Planck equations through gradient–log–density estimation

dc.contributor.authorMaoutsa, Dimitra
dc.contributor.authorReich, Sebastian
dc.contributor.authorOpper, Manfred
dc.date.accessioned2021-01-11T08:44:14Z
dc.date.available2021-01-11T08:44:14Z
dc.date.issued2020-07-22
dc.description.abstractFokker–Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment only in limited settings, and often it is inevitable to resort to numerical solutions. Here, we develop a computational approach for simulating the time evolution of Fokker–Planck solutions in terms of a mean field limit of an interacting particle system. The interactions between particles are determined by the gradient of the logarithm of the particle density, approximated here by a novel statistical estimator. The performance of our method shows promising results, with more accurate and less fluctuating statistics compared to direct stochastic simulations of comparable particle number. Taken together, our framework allows for effortless and reliable particle-based simulations of Fokker–Planck equations in low and moderate dimensions. The proposed gradient–log–density estimator is also of independent interest, for example, in the context of optimal control.en
dc.description.sponsorshipTU Berlin, Open-Access-Mittel – 2020en
dc.description.sponsorshipDFG, 318763901, SFB 1294: Datenassimilation: Die nahtlose Verschmelzung von Daten und Modellenen
dc.identifier.eissn1099-4300
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/12382
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-11223
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subject.ddc510 Mathematikde
dc.subject.otherstochastic systemsen
dc.subject.otherFokker-Planck equationen
dc.subject.otherinteracting particlesen
dc.subject.othermultiplicative noiseen
dc.subject.othergradient flowen
dc.subject.otherstochastic differential equationsen
dc.titleInteracting particle solutions of Fokker–Planck equations through gradient–log–density estimationen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.articlenumber802en
dcterms.bibliographicCitation.doi10.3390/e22080802en
dcterms.bibliographicCitation.issue8en
dcterms.bibliographicCitation.journaltitleEntropyen
dcterms.bibliographicCitation.originalpublishernameMDPIen
dcterms.bibliographicCitation.originalpublisherplaceBaselen
dcterms.bibliographicCitation.volume22en
tub.accessrights.dnbfreeen
tub.affiliationFak. 4 Elektrotechnik und Informatik>Inst. Softwaretechnik und Theoretische Informatik>FG Methoden der Künstlichen Intelligenzde
tub.affiliation.facultyFak. 4 Elektrotechnik und Informatikde
tub.affiliation.groupFG Methoden der Künstlichen Intelligenzde
tub.affiliation.instituteInst. Softwaretechnik und Theoretische Informatikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
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