A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks

Serge Gratton, Valentin Mercier, Elisa Riccietti, Philippe TOINT

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Résumé

Multi-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems. After a re-interpretation of multi-level methods from a block-coordinate point of view, we propose a multi-level algorithm for the solution of
nonlinear optimization problems and analyze its evaluation complexity. We apply it to the solution of partial differential equations using physics-informed neural networks (PINNs) and consider two different types of neural architectures, a generic feedforward network and a frequency-aware network. We show that our approach is
particularly effective if coupled with these specialized architectures and that this coupling results in better solutions and significant computational savings.
langue originaleAnglais
ÉditeurArxiv
Volume2305.14477
Etat de la publicationPublié - mai 2023

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