发表机构
School of Mathematics, University of Edinburgh（爱丁堡大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出FAMIS框架，利用归一化流非均匀混合进行自适应重要性采样，无需先验失效数据，通过斥力项增强多样性，实现复杂系统稀有事件概率的稳定高效估计。
AI 中文摘要
准确的稀有事件估计在计算上可能代价高昂。经典的自适应重要性采样（IS）方案通常依赖于限制性的提议分布族，并且在多种失效模式下可能表现不佳。我们提出了FAMIS，一种基于流的多种重要性采样（MIS）框架，该框架学习归一化流提议的非均匀混合以用于稀有事件估计。该方法不需要预采样的失效数据，也不需要事先知道失效模式的数量、位置或几何形状。相反，它通过顺序评估极限状态函数来自适应地学习混合分布。为了引导训练朝向失效域，FAMIS使用平滑的稀有事件代理和温和的目标序列。防御性探索混合改善了早期阶段的覆盖，Rao-Blackwellized更新自适应调整混合权重，而Jensen-Shannon斥力项促进了基分量之间的分离和多样性。最终的失效概率使用确定性混合MIS估计器计算。数值实验表明，FAMIS能够以更少的训练样本和模型评估准确逼近准最优IS密度，在复杂的可靠性问题中提供稳定的方差缩减。
英文摘要
Accurate rare-event estimation can be computationally expensive. Classical adaptive importance sampling (IS) schemes often rely on restrictive proposal families and can struggle under multiple failure modes. We propose FAMIS, a flow-based multiple importance sampling (MIS) framework that learns a nonuniform mixture of normalizing flow proposals for rare event estimation. The method does not require presampled failure data or prior knowledge of the number, location, or geometry of the failure modes. Instead, it adaptively learns the mixture through sequential evaluations of the limit state function. To guide training toward the failure domain, FAMIS uses a smooth rare-event surrogate and a tempered target sequence. A defensive exploration mixture improves early-stage coverage, a Rao Blackwellized update adapts the mixture weights, and a Jensen-Shannon repulsion term promotes separation and diversity among the base components. The final failure probability is computed with a deterministic-mixture MIS estimator. Numerical experiments demonstrate that FAMIS accurately approximates quasi-optimal IS densities with fewer training samples and model evaluations, providing stable variance reduction across complex reliability problems.
