fOGA: Orthogonal Greedy Algorithm for Fractional Laplace Equations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929514987126784 |
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| author | Shan, Ruitong Lee, Young Ju Jia, Jiwei |
| author_facet | Shan, Ruitong Lee, Young Ju Jia, Jiwei |
| contents | In this paper, we explore the finite difference approximation of the fractional Laplace operator in conjunction with a neural network method for solving it. We discretized the fractional Laplace operator using the Riemann-Liouville formula relevant to fractional equations. A shallow neural network was constructed to address the discrete fractional operator, coupled with the OGA algorithm. To validate the feasibility of our approach, we conducted numerical experiments, testing both the Laplace operator and the fractional Laplace operator, yielding favorable convergence results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16551 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | fOGA: Orthogonal Greedy Algorithm for Fractional Laplace Equations Shan, Ruitong Lee, Young Ju Jia, Jiwei Numerical Analysis In this paper, we explore the finite difference approximation of the fractional Laplace operator in conjunction with a neural network method for solving it. We discretized the fractional Laplace operator using the Riemann-Liouville formula relevant to fractional equations. A shallow neural network was constructed to address the discrete fractional operator, coupled with the OGA algorithm. To validate the feasibility of our approach, we conducted numerical experiments, testing both the Laplace operator and the fractional Laplace operator, yielding favorable convergence results. |
| title | fOGA: Orthogonal Greedy Algorithm for Fractional Laplace Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.16551 |