We propose a novel scale-invariant version of the mean and variance multi-level Monte Carlo estimate. The computation cost across grid levels is optimised using a normalized error based on t-statistics. By doing so, the algorithm achieves convergence independent of the physical scale at which the estimate is computed. The effectiveness of this algorithm is demonstrated through testing on a linear elastic example, where material uncertainty incorporating both heterogeneity and anisotropy is considered in the constitutive law.

翻译：我们提出了一种新颖的尺度不变均值与方差多层蒙特卡罗估计方法。通过基于t统计量的归一化误差来优化跨网格层的计算成本，该算法实现了与估计计算物理尺度无关的收敛性。通过考虑本构定律中同时包含异质性与各向异性的材料不确定性，在线弹性算例上的测试验证了该算法的有效性。