A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks
Machine Learning
2023-05-26 v2 Optimization and Control
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
Keywords
Cite
@article{arxiv.2305.14477,
title = {A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks},
author = {Serge Gratton and Valentin Mercier and Elisa Riccietti and Philippe L. Toint},
journal= {arXiv preprint arXiv:2305.14477},
year = {2023}
}