4 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…
Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter
Yuhan Wu, Jan Willem van Beek, Victorita Dolean +1
Deep learning-based hybrid iterative methods (DL-HIMs) integrate classical numerical solvers with neural operators, utilizing their complementary spectral biases to accelerate conv…
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…