Surrogate-Assisted Multilevel Importance Sampling Method for Failure Probability Estimation with Fidelity-Aware Strategies

Failure probability estimation is a core problem in risk and reliability analysis, made particularly demanding when forward simulations are computationally expensive and failure events are rare. Typically, costly high-fidelity forward models are complemented by lower-fidelity, inexpensive alternatives—e.g., simplified physics models or finite-element or finite-difference discretizations on coarser or sparse meshes. The multilevel Monte Carlo (MLMC) technique partially mitigates the fidelity–efficiency trade-off, but its Monte Carlo nature still entails large numbers of runs across parameter settings and fidelity levels. We propose an adaptive importance sampling framework that markedly reduces computational cost for rare-event estimation by constructing locally accurate surrogate models of the expensive simulator. By explicitly accounting for fidelity in surrogate modeling, failure boundary inference, and experimental design, the proposed method outperforms conventional approaches that treat fidelity merely as a scalar parameter. Numerical experiments on three representative problems demonstrate that the proposed approach delivers superior accuracy and substantially lower computational cost.