SGM-PINN: Sampling Graphical Models for Faster Training of Physics-Informed Neural Networks

TL;DR

SGM-PINN introduces a graph-based importance sampling method that accelerates Physics-Informed Neural Network training by focusing on critical data regions, achieving three times faster convergence.

Contribution

The paper presents a novel graph decomposition and importance sampling framework for PINNs, enhancing training efficiency and accuracy on parameterized problems.

Findings

Achieves 3x faster convergence than previous methods.

Effectively identifies critical regions for sampling.

Improves training speed and accuracy of PINNs.

Abstract

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.