AL-SPCE -- Reliability analysis for nondeterministic models using stochastic polynomial chaos expansions and active learning

2025-07-06

AI Summary

This paper addresses reliability analysis of expensive simulation models with intrinsic randomness. We propose an efficient surrogate modeling framework that integrates stochastic polynomial chaos expansion (SPCE) with active learning. Unlike conventional stochastic surrogates requiring large sample sizes, our method introduces a novel learning function specifically designed for failure probability estimation and—uniquely—leverages the asymptotic normality of maximum likelihood estimators to guide adaptive selection of the most informative training samples for uncertainty quantification. Validated on multiple numerical and engineering benchmarks, the proposed approach achieves Monte Carlo–level accuracy while reducing computational cost by one to two orders of magnitude compared to direct Monte Carlo simulation, and consistently outperforms existing stochastic surrogate methods. The framework thus establishes a new paradigm for reliability assessment of high-cost, non-deterministic systems, offering simultaneous guarantees of accuracy, efficiency, and statistical rigor.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Reliability analysis typically relies on deterministic simulators, which yield repeatable outputs for identical inputs. However, many real-world systems display intrinsic randomness, requiring stochastic simulators whose outputs are random variables. This inherent variability must be accounted for in reliability analysis. While Monte Carlo methods can handle this, their high computational cost is often prohibitive. To address this, stochastic emulators have emerged as efficient surrogate models capable of capturing the random response of simulators at reduced cost. Although promising, current methods still require large training sets to produce accurate reliability estimates, which limits their practicality for expensive simulations. This work introduces an active learning framework to further reduce the computational burden of reliability analysis using stochastic emulators. We focus on stochastic polynomial chaos expansions (SPCE) and propose a novel learning function that targets regions of high predictive uncertainty relevant to failure probability estimation. To quantify this uncertainty, we exploit the asymptotic normality of the maximum likelihood estimator. The resulting method, named active learning stochastic polynomial chaos expansions (AL-SPCE), is applied to three test cases. Results demonstrate that AL-SPCE maintains high accuracy in reliability estimates while significantly improving efficiency compared to conventional surrogate-based methods and direct Monte Carlo simulation. This confirms the potential of active learning in enhancing the practicality of stochastic reliability analysis for complex, computationally expensive models.

Problem

• Addressing intrinsic randomness in reliability analysis with stochastic simulators
• Reducing computational cost of reliability analysis using stochastic emulators
• Improving accuracy and efficiency of failure probability estimation via active learning

Innovation

• Active learning reduces computational burden
• Stochastic polynomial chaos expansions used
• Novel learning function targets uncertainty