Título:
A deep first-order system least squares method for solving elliptic PDEs.
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Autor:
Bersetche, Francisco M.
Borthagaray, Juan Pablo
Borthagaray, Juan Pablo
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Tipo de documento:
Preprint
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Palabras clave:
Numerical Analysis
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Año de publicación:
2022
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Resumen:
We propose a First-Order System Least Squares (FOSLS) method based on deep-learning for numerically solving second-order elliptic PDEs. The method we propose is capable of dealing with either variational and non-variational problems, and because of its meshless nature, it can also deal with problems posed in high-dimensional domains. We prove the Γ-convergence of the neural network approximation towards the solution of the continuous problem, and extend the convergence proof to some well-known related methods. Finally, we present several numerical examples illustrating the performance of our discretization.
Descripción:
También publicado en Computers & Mathematics with Applications, vol. 129, jan. 2023, pp. 136-150. DOI: 10.1016/j.camwa.2022.11.014.
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Editorial:
arXiv
EN:
Mathematics. Numerical Analysis (math.NA), arXiv:2204.07227v2, dec 2022, pp 1-23
Financiadores:
Francisco M. Bersetche ha sido financiado en parte por una beca postdoctoral de PEDECIBA y la beca ANPCyT PICT 2018-3017.
Citación:
Bersetche, F. y Borthagaray, J. A deep first-order system least squares method for solving elliptic PDEs. [Preprint]. Publicado en: Mathematics. Numerical Analysis (math.NA). 2022, pp. 1-23. arXiv:2204.07227v2. DOI: 10.48550/arXiv.2204.07227.
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Licencia:
Licencia Creative Commons Atribución (CC - By 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| BB22.pdf | Preprint | 763.15 KB | Adobe PDF |