# Accounting for Uncertainty in Machine Learning Surrogates: A Gauss-Hermite Quadrature Approach to Reliability Analysis

arXiv: https://arxiv.org/abs/2509.18128 · HTML: https://mlsanity.com/paper/2509.18128/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 54 references that are in the map.
- First posted on arXiv 11 Sep 2025.

## Builds on (most cited first, 5 of 5)

- [Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial](https://mlsanity.com/paper/2305.04933/) (2023)
- [Machine Learning for Reliability Engineering and Safety Applications: Review of Current Status and Future Opportunities](https://mlsanity.com/paper/2008.08221/) (2020)
- [Efficient Calibration for Imperfect Computer Models](https://mlsanity.com/paper/1507.07280/) (2015)
- [Surrogate modeling based on resampled polynomial chaos expansions](https://mlsanity.com/paper/1810.09116/) (2018)
- [Cutting the Double Loop: Theory and Algorithms for Reliability-Based Design Optimization with Statistical Uncertainty](https://mlsanity.com/paper/1806.00048/) (2018)

## Abstract (arXiv)

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.