Rare event simulation and rare event probability estimation are important tasks within the analysis of systems subject to uncertainty and randomness. Simultaneously, accurately estimating rare event probabilities is an inherently difficult task that calls for dedicated tools and methods. One way to improve estimation efficiency on difficult rare event estimation problems is to leverage gradients of the computational model representing the system in consideration, e.g., to explore the rare event faster and more reliably. We present a novel approach for estimating rare event probabilities using such model gradients by drawing on a technique to generate samples from non-normalized posterior distributions in Bayesian inference - the Stein variational gradient descent. We propagate samples generated from a tractable input distribution towards a near-optimal rare event importance sampling distribution by exploiting a similarity of the latter with Bayesian posterior distributions. Sample propagation takes the shape of passing samples through a sequence of invertible transforms such that their densities can be tracked and used to construct an unbiased importance sampling estimate of the rare event probability - the Stein variational rare event estimator. We discuss settings and parametric choices of the algorithm and suggest a method for balancing convergence speed with stability by choosing the step width or base learning rate adaptively. We analyze the method's performance on several analytical test functions and two engineering examples in low to high stochastic dimensions ($d = 2 - 869$) and find that it consistently outperforms other state-of-the-art gradient-based rare event simulation methods.

翻译：稀有事件模拟及其概率估计是分析受不确定性和随机性影响系统的重要任务。与此同时，准确估计稀有事件概率本质上是一项艰巨的任务，需要专门的工具与方法。提升困难稀有事件估计问题中估计效率的一种途径是利用表征所考虑系统的计算模型的梯度，例如，以更快、更可靠地探索稀有事件。我们提出一种利用此类模型梯度估计稀有事件概率的新方法，该方法借鉴了贝叶斯推断中从非归一化后验分布生成样本的技术——Stein变分梯度下降。通过挖掘稀有事件重要采样分布与贝叶斯后验分布之间的相似性，我们将从易处理输入分布生成的样本向近似最优的稀有事件重要采样分布传播。样本传播采用通过一系列可逆变换传递样本的形式，从而可追踪其密度，并用于构建稀有事件概率的无偏重要采样估计——即Stein变分稀有事件估计量。我们讨论了该算法的参数设置与选择，并提出一种通过自适应选择步长或基学习率来平衡收敛速度与稳定性的方法。我们在低维至高维随机维度（$d = 2 - 869$）下，通过多个分析测试函数及两个工程实例分析了该方法的表现，发现其始终优于其他最先进的基于梯度的稀有事件模拟方法。