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Physically guided deep learning solver for time-dependent Fokker–Planck equation
Yang Zhang1,2; Ka-Veng Yuen1,2
2022-08-29
Source PublicationINTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
ISSN0020-7462
Volume147Pages:104202
Abstract

The Fokker–Planck (FP) equation is of significant relevance in stochastic dynamics. To solve the FP equation, this paper proposes a physically guided deep learning-based method. The proposed method uses physical modeling as the constraint for guiding the deep neural networks to learn the solutions of the FP equation from unlabeled data. Four numerical examples were used to verify the accuracy and effectiveness of the proposed method for solving linear FP equations and nonlinear FP equations. Moreover, we examined the robustness of the trained model. Finally, extra observation data was used to replace the boundary conditions and initial conditions in complicated forms. Meanwhile, the effect of missing boundary conditions or initial conditions to the proposed method was further analyzed. The results demonstrated that observation data can be used as promising substitution for the initial and boundary conditions while the proposed method can still obtain accurate numerical solutions in the absence of some conditions.

KeywordFokker–planck Neural Network Physical Constraint Robustness
DOI10.1016/j.ijnonlinmec.2022.104202
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMechanics
WOS SubjectMechanics
WOS IDWOS:000864416800011
PublisherPERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Scopus ID2-s2.0-85138772723
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Document TypeJournal article
CollectionTHE STATE KEY LABORATORY OF INTERNET OF THINGS FOR SMART CITY (UNIVERSITY OF MACAU)
Faculty of Science and Technology
Corresponding AuthorKa-Veng Yuen
Affiliation1.State Key Laboratory of Internet of Things for Smart City and Department of Civil and Environmental Engineering, University of Macau, Macau, China
2.Guangdong-Hong Kong-Macau Joint Laboratory for Smart Cities, University of Macau, Macau, China
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Yang Zhang,Ka-Veng Yuen. Physically guided deep learning solver for time-dependent Fokker–Planck equation[J]. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2022, 147, 104202.
APA Yang Zhang., & Ka-Veng Yuen (2022). Physically guided deep learning solver for time-dependent Fokker–Planck equation. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 147, 104202.
MLA Yang Zhang,et al."Physically guided deep learning solver for time-dependent Fokker–Planck equation".INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 147(2022):104202.
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