论文标题
通过多级蒙特卡洛法量化不确定的系统输出 - 分布和鲁棒性措施
Quantifying uncertain system outputs via the multi-level Monte Carlo method -- distribution and robustness measures
论文作者
论文摘要
在这项工作中，我们考虑了通过MLMC方法估算估计复杂随机差异模型的输出量的概率分布，分位数或条件期望的问题。我们遵循（参考）的方法，该方法将上述数量的估计估计到适当的参数期望的计算。在这项工作中，我们提出了用于估计此类数量的新型可计算误差估计器，然后将其用于最佳调整MLMC层次结构，以延续类型的自适应算法。我们证明了在一系列数值测试案例中自适应延续MLMC的效率和鲁棒性。
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential models by the MLMC method. We follow the approach of (reference), which recasts the estimation of the above quantities to the computation of suitable parametric expectations. In this work, we present novel computable error estimators for the estimation of such quantities, which are then used to optimally tune the MLMC hierarchy in a continuation type adaptive algorithm. We demonstrate the efficiency and robustness of our adaptive continuation-MLMC in an array of numerical test cases.
