This paper studies the utility of techniques within uncertainty quantification, namely spectral projection and polynomial chaos expansion, in reducing sampling needs for characterizing acoustic metamaterial dispersion band responses given stochastic material properties and geometric defects. A novel method of encoding geometric defects in an interpretable, resolution independent is showcased in the formation of input space probability distributions. Orders of magnitude sampling reductions down to $\sim10^0$ and $\sim10^1$ are achieved in the 1D and 7D input space scenarios respectively while maintaining accurate output space probability distributions through combining Monte Carlo, quadrature rule, and sparse grid sampling with surrogate model fitting.

翻译：本文研究了不确定性量化技术（即谱投影法和多项式混沌展开）在降低表征声学超材料频散能带响应采样需求方面的效用，其中材料属性和几何缺陷具有随机性。提出了一种以可解释、分辨率无关方式编码几何缺陷的新方法，用于构建输入空间概率分布。通过结合蒙特卡洛方法、求积法则和稀疏网格采样与代理模型拟合，在一维和七维输入空间场景中分别实现了约$10^0$和$10^1$量级的采样量级缩减，同时保持了输出空间概率分布的准确性。