Título:
A deep first-order system least squares method for the obstacle problem
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Autor:
Acosta, Gabriel
Belén, Eugenia
Bersetche, Francisco M.
Borthagaray, Juan Pablo
Belén, Eugenia
Bersetche, Francisco M.
Borthagaray, Juan Pablo
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Tipo de documento:
Otro
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Año de publicación:
2025
Contenido:
Resumen:
We propose a deep learning approach to the obstacle problem inspired by the rstorder
system least-squares (FOSLS) framework. This method reformulates the problem as a
convex minimization task; by simultaneously approximating the solution, gradient, and Lagrange
multiplier, our approach provides a
exible, mesh-free alternative that scales e ciently to highdimensional
settings. Key theoretical contributions include the coercivity and local Lipschitz
continuity of the proposed least-squares functional, along with convergence guarantees via Γ-convergence theory under mild regularity assumptions. Numerical experiments in dimensions up
to 20 demonstrate the method's robustness and scalability, even on non-Lipschitz domains.
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Financiadores:
Proyecto Fondo Clemente Estable (modalidad II), FCE_3_2022_1_172393.
Citación:
Acosta, G., Belén, E., Bersetche, F. y otros. A deep first-order system least squares method for the obstacle problem [en línea] 2025. 26 p.
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Licencia:
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
Colecciones:
| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| ABBB25.pdf | Trabajo de investigación | 1.38 MB | Adobe PDF |