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

arXiv: https://arxiv.org/abs/2407.07358 · HTML: https://mlsanity.com/paper/2407.07358/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 10 Jul 2024.

## Builds on (most cited first, 12 of 12)

- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Not All Samples Are Created Equal: Deep Learning with Importance Sampling](https://mlsanity.com/paper/1803.00942/) (2018)
- [Efficient training of physics-informed neural networks via importance sampling](https://mlsanity.com/paper/2104.12325/) (2021)
- [Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling](https://mlsanity.com/paper/2207.02338/) (2022)
- [Biased Importance Sampling for Deep Neural Network Training](https://mlsanity.com/paper/1706.00043/) (2017)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [SPADE: A Spectral Method for Black-Box Adversarial Robustness Evaluation](https://mlsanity.com/paper/2102.03716/) (2021)
- [Graph Clustering using Effective Resistance](https://mlsanity.com/paper/1711.06530/) (2017)
- [HyperEF: Spectral Hypergraph Coarsening by Effective-Resistance Clustering](https://mlsanity.com/paper/2210.14813/) (2022)

## Abstract (arXiv)

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× faster convergence compared to prior state-of-the-art sampling methods.