4 papers
Two-level deep domain decomposition method
Victorita Dolean, Serge Gratton, Alexander Heinlein +1
This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural…
Refining asymptotic complexity bounds for nonconvex optimization methods, including why steepest descent is rather than
Serge Gratton, Chee-Khian Sim, Philippe L. Toint
We revisit the standard ``telescoping sum'' argument ubiquitous in the final steps of analyzing evaluation complexity of algorithms for smooth nonconvex optimization, and obtain a…
A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks
Serge Gratton, Valentin Mercier, Elisa Riccietti +1
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…
A coarse space acceleration of deep-DDM
Valentin Mercier, Serge Gratton, Pierre Boudier
The use of deep learning methods for solving PDEs is a field in full expansion. In particular, Physical Informed Neural Networks, that implement a sampling of the physical domain a…