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math.NA2026
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…
math.NA2026
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…
math.NA2007
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…