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Pré-Publication, Document De Travail Année : 2023

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

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 show on a few test problems that the approach results in better solutions and significant computational savings.
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Dates et versions

hal-04104450 , version 1 (24-05-2023)

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  • HAL Id : hal-04104450 , version 1

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Serge Gratton, Valentin Mercier, Elisa Riccietti, Philippe L Toint. A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks. 2023. ⟨hal-04104450⟩
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