# Machine learning-based system reliability analysis with Gaussian Process Regression

arXiv: https://arxiv.org/abs/2403.11125 · HTML: https://mlsanity.com/paper/2403.11125/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 68 references that are in the map.
- First posted on arXiv 17 Mar 2024.

## Builds on (most cited first, 6 of 6)

- [Complementary Fusion of Multi-Features and Multi-Modalities in Sentiment Analysis](https://mlsanity.com/paper/1904.08138/) (2019)
- [Comprehensive evaluation of Mal-API-2019 dataset by machine learning in malware detection](https://mlsanity.com/paper/2403.02232/) (2024)
- [Deep Learning-Based Strategy for Macromolecules Classification with Imbalanced Data from Cellular Electron Cryotomography](https://mlsanity.com/paper/1908.09993/) (2019)
- [REAK: Reliability analysis through Error rate-based Adaptive Kriging](https://mlsanity.com/paper/2002.01110/) (2020)
- [Learning Robust Heterogeneous Signal Features from Parallel Neural Network for Audio Sentiment Analysis](https://mlsanity.com/paper/1811.08065/) (2018)
- [Value of Information Analysis via Active Learning and Knowledge Sharing in Error-Controlled Adaptive Kriging](https://mlsanity.com/paper/2002.02354/) (2020)

## Built on by (most cited first, 2 of 2)

- [Comprehensive Survey of Model Compression and Speed up for Vision Transformers](https://mlsanity.com/paper/2404.10407/) (2024)
- [Cross-Modal Domain Adaptation in Brain Disease Diagnosis: Maximum Mean Discrepancy-based Convolutional Neural Networks](https://mlsanity.com/paper/2405.03235/) (2024)

## Abstract (arXiv)

Machine learning-based reliability analysis methods have shown great advancements for their computational efficiency and accuracy. Recently, many efficient learning strategies have been proposed to enhance the computational performance. However, few of them explores the theoretical optimal learning strategy. In this article, we propose several theorems that facilitates such exploration. Specifically, cases that considering and neglecting the correlations among the candidate design samples are well elaborated. Moreover, we prove that the well-known U learning function can be reformulated to the optimal learning function for the case neglecting the Kriging correlation. In addition, the theoretical optimal learning strategy for sequential multiple training samples enrichment is also mathematically explored through the Bayesian estimate with the corresponding lost functions. Simulation results show that the optimal learning strategy considering the Kriging correlation works better than that neglecting the Kriging correlation and other state-of-the art learning functions from the literatures in terms of the reduction of number of evaluations of performance function. However, the implementation needs to investigate very large computational resource.