6 papers
Two-level domain-decomposition AdaGrad method for scalable training of graph neural networks
Laurynas Varnas, Julien Herrmann, Alexander Heinlein +2
Graph neural networks (GNNs) have emerged as a powerful framework for learning from graph-structured data. However, their efficient training remains challenging, particularly in di…
Lipschitz bounds for integral kernels
Justin Reverdi, Sixin Zhang, Fabrice Gamboa +1
Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are close…
Toward an Operational GNN-Based Multimesh Surrogate for Fast Flood Forecasting
Valentin Mercier, Serge Gratton, Lapeyre Corentin +1
Operational flood forecasting still relies on high-fidelity two-dimensional hydraulic solvers, but their runtime can be prohibitive for rapid decision support on large urban floodp…
Multi-Preconditioned LBFGS for Training Finite-Basis PINNs
Marc Salvadó-Benasco, Aymane Kssim, Alexander Heinlein +3
A multi-preconditioned LBFGS (MP-LBFGS) algorithm is introduced for training finite-basis physics-informed neural networks (FBPINNs). The algorithm is motivated by the nonlinear ad…
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…
Computing the Conditioning of the Components of a Linear Least Squares Solution
Marc Baboulin, Jack Dongarra, Serge Gratton +1
In this paper, we address the accuracy of the results for the overdetermined full rank linear least squares problem. We recall theoretical results obtained in Arioli, Baboulin and…