Trend to equilibrium for the kinetic Fokker-Planck equation via the neural network approach

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dc.creatorHwang, Hyung Ju
dc.creatorJang, Jin Woo
dc.creatorJo, Hyeontae
dc.creatorLee, Jae Yong
dc.date.accessioned2020-07-14T17:14:44Z
dc.date.available2020-07-14T17:14:44Z
dc.date.created2020-10-15
dc.description.abstractenglishThe issue of the relaxation to equilibrium has been at the core of the kinetic theory of rarefied gas dynamics. In the paper, we introduce the Deep Neural Network (DNN) approximated solutions to the kinetic Fokker-Planck equation in a bounded interval and study the large-time asymptotic behavior of the solutions and other physically relevant macroscopic quantities. We impose the varied types of boundary conditions including the inflow-type and the reflection-type boundaries as well as the varied diffusion and friction coefficients and study the boundary effects on the asymptotic behaviors. These include the predictions on the large-time behaviors of the pointwise values of the particle distribution and the macroscopic physical quantities including the total kinetic energy, the entropy, and the free energy. We also provide the theoretical supports for the pointwise convergence of the neural network solutions to the a priori analytic solutions. We use the library PyTorch, the activation function tanh between layers, and the Adam optimizer for the Deep Learning algorithm.spa
dc.format.extent25 páginasspa
dc.format.mimetypeapplication/pdfspa
dc.identifier.doihttps://doi.org/10.1016/j.jcp.2020.109665spa
dc.identifier.issn0021-9991spa
dc.identifier.otherhttps://www.sciencedirect.com/science/article/pii/S0021999120304393?via%3Dihubspa
dc.identifier.urihttps://hdl.handle.net/20.500.12010/10493
dc.publisherScience Directeng
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.sourcereponame:Expeditio Repositorio Institucional UJTLspa
dc.sourceinstname:Universidad de Bogotá Jorge Tadeo Lozanospa
dc.subjectEcuación de Fokker-Planckspa
dc.subjectTeoría cinética de los gasesspa
dc.subjectInteligencia artificialspa
dc.subject.keywordFokker-Planck equationspa
dc.subject.keywordAsymptotic behavior of solutionsspa
dc.subject.keywordKinetic theory of gasesspa
dc.subject.keywordArtificial intelligencespa
dc.subject.lembSíndrome respiratorio agudo gravespa
dc.subject.lembCOVID-19spa
dc.subject.lembSARS-CoV-2spa
dc.subject.lembCoronavirusspa
dc.titleTrend to equilibrium for the kinetic Fokker-Planck equation via the neural network approachspa
dc.type.hasversioninfo:eu-repo/semantics/acceptedVersionspa
dc.type.localArtículospa

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