A deep first-order system least squares method for the obstacle problem
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.
| 2025 | |
| Proyecto Fondo Clemente Estable (modalidad II), FCE_3_2022_1_172393. | |
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/51260 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
