Accounting for Uncertainty in Machine Learning Surrogates: A Gauss-Hermite Quadrature Approach to Reliability Analysis
This work addresses reliability analysis for physics-based models using surrogates, but it is incremental as it builds on existing methods like FORM/SORM.
The study tackled the problem of epistemic uncertainty from machine learning surrogates in reliability analysis by proposing a Gauss-Hermite quadrature approach to decouple nested uncertainties, resulting in more accurate and trustworthy predictions while maintaining computational efficiency, as demonstrated in three examples.
Machine learning surrogates are increasingly employed to replace expensive computational models for physics-based reliability analysis. However, their use introduces epistemic uncertainty from model approximation errors, which couples with aleatory uncertainty in model inputs, potentially compromising the accuracy of reliability predictions. This study proposes a Gauss-Hermite quadrature approach to decouple these nested uncertainties and enable more accurate reliability analysis. The method evaluates conditional failure probabilities under aleatory uncertainty using First and Second Order Reliability Methods and then integrates these probabilities across realizations of epistemic uncertainty. Three examples demonstrate that the proposed approach maintains computational efficiency while yielding more trustworthy predictions than traditional methods that ignore model uncertainty.