A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks - Calcul Intensif, Simulation, Optimisation Access content directly
Preprints, Working Papers, ... Year : 2023

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

Abstract

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 and versions

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

Identifiers

  • HAL Id : hal-04104450 , version 1

Cite

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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