论文标题
大偏差理论的自适应重要性抽样对罕见事件的高维度
Large deviation theory-based adaptive importance sampling for rare events in high dimensions
论文作者
论文摘要
我们提出了一种准确估计罕见事件或失败概率的方法，以高度昂贵的数值模型。提出的方法结合了大偏差理论和自适应重要性抽样的思想。重要性采样器使用跨凝结方法来找到最佳的高斯偏见分布，并重用在整个过程中进行的所有样本，以供目标概率估计以及更新偏见分布。大型偏差理论用于通过优化问题解决方案找到良好的初始偏见分布。此外，它用于识别低维子空间，该子空间最有用的事件概率提供了信息。该子空间用于跨熵方法，该方法已知在更高维度上失去效率。所提出的方法不需要平滑指示函数，也不需要涉及数值调整参数。我们使用三个示例将该方法与基于跨透明的最先进的重要性抽样方案进行了比较：高维失效概率估计基准基准，由扩散方程控制的问题以及一个由一个空间尺寸中的时间依赖性浅水系统控制的海啸问题。
We propose a method for the accurate estimation of rare event or failure probabilities for expensive-to-evaluate numerical models in high dimensions. The proposed approach combines ideas from large deviation theory and adaptive importance sampling. The importance sampler uses a cross-entropy method to find an optimal Gaussian biasing distribution, and reuses all samples made throughout the process for both, the target probability estimation and for updating the biasing distributions. Large deviation theory is used to find a good initial biasing distribution through the solution of an optimization problem. Additionally, it is used to identify a low-dimensional subspace that is most informative of the rare event probability. This subspace is used for the cross-entropy method, which is known to lose efficiency in higher dimensions. The proposed method does not require smoothing of indicator functions nor does it involve numerical tuning parameters. We compare the method with a state-of-the-art cross-entropy-based importance sampling scheme using three examples: a high-dimensional failure probability estimation benchmark, a problem governed by a diffusion equation, and a tsunami problem governed by the time-dependent shallow water system in one spatial dimension.
