Solving Fokker-Planck equation using deep learning Article Swipe
Yong Xu
,
Hao Zhang
,
Yongge Li
,
Kuang Zhou
,
Qi Liu
,
Jürgen Kurths
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1063/1.5132840
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1063/1.5132840
The probability density function of stochastic differential equations is governed by the Fokker-Planck (FP) equation. A novel machine learning method is developed to solve the general FP equations based on deep neural networks. The proposed algorithm does not require any interpolation and coordinate transformation, which is different from the traditional numerical methods. The main novelty of this paper is that penalty factors are introduced to overcome the local optimization for the deep learning approach, and the corresponding setting rules are given. Meanwhile, we consider a normalization condition as a supervision condition to effectively avoid that the trial solution is zero. Several numerical examples are presented to illustrate performances of the proposed algorithm, including one-, two-, and three-dimensional systems. All the results suggest that the deep learning is quite feasible and effective to calculate the FP equation. Furthermore, influences of the number of hidden layers, the penalty factors, and the optimization algorithm are discussed in detail. These results indicate that the performances of the machine learning technique can be improved through constructing the neural networks appropriately.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1063/1.5132840
- OA Status
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- Cited By
- 135
- References
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- OpenAlex ID
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https://openalex.org/W3002873949Canonical identifier for this work in OpenAlex
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https://doi.org/10.1063/1.5132840Digital Object Identifier
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Solving Fokker-Planck equation using deep learningWork title
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2020Year of publication
- Publication date
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2020-01-01Full publication date if available
- Authors
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Yong Xu, Hao Zhang, Yongge Li, Kuang Zhou, Qi Liu, Jürgen KurthsList of authors in order
- Landing page
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https://doi.org/10.1063/1.5132840Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/1910.10503Direct OA link when available
- Concepts
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Fokker–Planck equation, Statistical physics, Physics, Artificial intelligence, Computer science, Mathematics, Partial differential equation, Mathematical analysisTop concepts (fields/topics) attached by OpenAlex
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135Total citation count in OpenAlex
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2025: 35, 2024: 30, 2023: 22, 2022: 30, 2021: 12Per-year citation counts (last 5 years)
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43Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| primary_location.source.display_name | Chaos An Interdisciplinary Journal of Nonlinear Science |
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| primary_location.source.host_organization_name | American Institute of Physics |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310320257 |
| primary_location.source.host_organization_lineage_names | American Institute of Physics |
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| primary_location.raw_source_name | Chaos: An Interdisciplinary Journal of Nonlinear Science |
| primary_location.landing_page_url | https://doi.org/10.1063/1.5132840 |
| publication_date | 2020-01-01 |
| publication_year | 2020 |
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