XXIX/XIX Congreso de Ecuaciones Diferenciales y Aplicaciones / Congreso de Matemática Aplicada - CEDYA/CMA 2026, Valencia (España). 06-10 julio 2026
Resumen:
Homogenization theory connects microscopic structure and macroscopic behavior in heterogeneous media. Its numerical treatment becomes rapidly expensive when the oscillation scale ε is small, as classical solvers
require extremely fine meshes and often rely on explicit cell problems that may be unavailable or hard to define.
This communication presents a multi-scale Physics-Informed Neural Network (PINN) framework using neural networks as a structured ansatz for the asymptotic decomposition itself. The model simultaneously learns the homogenized component, first and second-order correctors, and the effective behavior, while enforcing boundary conditions, periodicity, and residual consistency in a single optimization process. [...]
Fecha de publicación: 06-jul-2026
Cita:
L. Bustinduy de la Guerra, E. Mompó, M. Villanueva Pesqueira, "Multi-scale Decomposition PINNs for Direct and Inverse Homogenization Problems", presentado en XXIX/XIX Congreso de Ecuaciones Diferenciales y Aplicaciones / Congreso de Matemática Aplicada - CEDYA/CMA 2026, Valencia, España, 06-10 julio 2026
IIT-26-163C_abstract
