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：稀有事件模拟与稀有事件概率估计是分析受不确定性和随机性影响的系统时的重要任务。同时，准确估计稀有事件概率本质上是一项困难的工作，需要专门的工具和方法。在困难的稀有事件估计问题上提高估计效率的一种途径是利用代表所考虑系统的计算模型的梯度，例如，以更快、更可靠的方式探索稀有事件。我们提出了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——斯坦变分梯度下降。我们通过利用近最优稀有事件重要性采样分布与贝叶斯后验分布的相似性，将从一个易处理的输入分布生成的样本传播至该近优分布。样本传播的形式是让样本通过一系列可逆变换，从而可以追踪其密度并用于构建稀有事件概率的无偏重要性采样估计量——斯坦变分稀有事件估计量。我们讨论了该算法的设置和参数选择，并提出了一种通过自适应选择步长或基础学习率来平衡收敛速度与稳定性的方法。我们在多个解析测试函数和两个低至高随机维度（$d = 2 - 869$）的工程实例上分析了该方法的性能，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。