Synthetic minority over-sampling technique (SMOTE)-enhanced adaptive sampling physics-informed neural networks for efficient reliability analysis

Although significant progress has been achieved in adaptive sampling methods for reliability analysis based on Physics-informed neural networks (PINNs), computational redundancy caused by fixed-size candidate sample sets and the sparsity of samples near the failure domain still constrain their accuracy and efficiency. To overcome these limitations, this paper proposes synthetic minority over-sampling technique (SMOTE)-enhanced adaptive sampling PINNs for efficient reliability analysis (SAS-PINN-RA). Two key mechanisms are introduced: (1) a dynamically updated candidate set that balances global exploration and local refinement by combining globally drawn random samples with near-failure samples carried over from the previous iteration; and (2) a near-failure domain oversampling strategy, where SMOTE is employed to enrich the sample density around the limit state, continuously improving the representation of critical regions. During training, adaptive samples are updated periodically rather than per epoch, reducing the sampling frequency while allowing the model to converge on the current training set between updates. Systematic verification on five benchmark problems demonstrates that SAS-PINN-RA achieves accurate structural response predictions in the near-failure region and efficient failure probability estimation without requiring extensive finite element analyses, highlighting its high computational efficiency and practical potential for engineering applications.