AI 中文总结
该研究提出结合多级分解与交互粒子系统框架的新算法，可高效估计失效概率，收敛速率快于经典多级蒙特卡洛算法且与当前最优技术相当，还通过数值实验验证了结果的正确性。
AI 中文摘要
我们提出了一种新方法，将多级分解与交互粒子系统（Interacting Particle Systems）框架相结合，以计算给定感兴趣量取特定预设值之上或之下的概率。通过应用序贯抽样方案，该算法能够实现比经典多级蒙特卡洛（Multilevel Monte Carlo）算法更快的收敛速率，且与当前最先进技术相当，同时具有维度无关性。此外，该算法生成的样本点形成一条序列，集中在感兴趣量的临界值附近。我们的结果得到了严格证明，并通过数值实验进行了验证。
英文摘要
We propose a novel method that combines a multilevel decomposition with the framework of Interacting Particle Systems to compute the probability that given quantities of interest take values above or below a certain pre-specified value. Through the application of a sequential sampling scheme, the algorithm is able to achieve convergence rates faster than those achieved by the classical Multilevel Monte Carlo algorithm, and competes with the current state of the art techniques, while also being dimension independent. Furthermore, the sample points generated by the algorithm form a sequence which concentrates near the critical value of the quantity of interest. Our results are rigorously established and later verified through numerical experiments.
