Verification solutions for uncertainty quantification are presented for time dependent transport problems where $c$, the scattering ratio, is uncertain. The method of polynomial chaos expansions is employed for quick and accurate calculation of the quantities of interest and uncollided solutions are used to treat part of the uncertainty calculation analytically. We find that approximately six moments in the polynomial expansion are required to represent the solutions to these problems accurately. Additionally, the results show that if the uncertainty interval spans c=1, which means it is uncertain whether the system is multiplying or not, the confidence interval will grow in time. Finally, since the QoI is a strictly increasing function, the percentile values are known and can be used to verify the accuracy of the expansion. These results can be used to test UQ methods for time-dependent transport problems.

翻译：针对散射比c不确定的时间依赖输运问题，本文给出了不确定性量化的验证解。采用多项式混沌展开法快速精确计算关注量，并利用非碰撞解解析处理部分不确定性计算。研究表明，约需六个多项式展开矩即可准确表征此类问题的解。此外，结果表明若不确定性区间跨越c=1（即系统是否具备倍增特性存在不确定性），置信区间将随时间增长。最后，由于关注量为严格递增函数，其百分位值已知，可用于验证展开法的准确性。这些结果可用于检验时间依赖输运问题的不确定性量化方法。