SGM-PINN: Sampling Graphical Models for Faster Training of Physics-Informed Neural Networks
This addresses training efficiency for PINNs in parameterized problems, but it is incremental as it builds on existing sampling techniques.
The paper tackled the slow training of Physics-Informed Neural Networks (PINNs) by introducing a graph-based importance sampling framework, achieving 3x faster convergence compared to prior methods.
SGM-PINN is a graph-based importance sampling framework to improve the training efficacy of Physics-Informed Neural Networks (PINNs) on parameterized problems. By applying a graph decomposition scheme to an undirected Probabilistic Graphical Model (PGM) built from the training dataset, our method generates node clusters encoding conditional dependence between training samples. Biasing sampling towards more important clusters allows smaller mini-batches and training datasets, improving training speed and accuracy. We additionally fuse an efficient robustness metric with residual losses to determine regions requiring additional sampling. Experiments demonstrate the advantages of the proposed framework, achieving $3\times$ faster convergence compared to prior state-of-the-art sampling methods.