Residential College | false |
Status | 已發表Published |
Physically guided deep learning solver for time-dependent Fokker–Planck equation | |
Yang Zhang1,2; Ka-Veng Yuen1,2 | |
2022-08-29 | |
Source Publication | INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS |
ISSN | 0020-7462 |
Volume | 147Pages: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. |
Keyword | Fokker–planck Neural Network Physical Constraint Robustness |
DOI | 10.1016/j.ijnonlinmec.2022.104202 |
URL | View the original |
Indexed By | SCIE |
Language | 英語English |
WOS Research Area | Mechanics |
WOS Subject | Mechanics |
WOS ID | WOS:000864416800011 |
Publisher | PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND |
Scopus ID | 2-s2.0-85138772723 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | THE STATE KEY LABORATORY OF INTERNET OF THINGS FOR SMART CITY (UNIVERSITY OF MACAU) Faculty of Science and Technology |
Corresponding Author | Ka-Veng Yuen |
Affiliation | 1.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 Affilication | University of Macau |
Corresponding Author Affilication | University 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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