  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.
