裂变矩阵方法的不确定性量化：一个严格的数学框架与计算高效的替代方案
Uncertainty Quantification for the Fission Matrix Method: A Rigorous Mathematical Framework and Computationally Efficient Alternatives
- Colorado School of Mines（科罗拉多矿业学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文为裂变矩阵方法提出全协方差Delta不确定性传播框架，并用两种低成本替代方案验证，推荐对角Delta方法作为实用默认选择。
AI中文摘要：
裂变矩阵（FM）方法将中子输运重新表述为矩阵形式，从而能够利用预先计算的蒙特卡罗系数数据库进行快速、基于插值的反应堆计算。将底层蒙特卡罗统计不确定性传播到FM特征值和特征向量很少是严格的：先前的方法假设系数独立，而不根据其实际协方差对此进行检验。本工作推导了一个全协方差Delta方法框架，用于将不确定性传播到keff和裂变源，并使用JSI TRIGA Mark-II反应堆的OpenMC模型，通过两种更便宜的替代方案（对角协方差近似和FM系数的直接重采样）对其进行评估。对于全棒提出情况，这三种估计器与100次独立蒙特卡罗运行的经验基准在keff上相差在5.7%以内，在裂变源上相差在1%以内。对角近似的偏差符号在两个统计水平之间翻转，因此必须逐案检查。采用全局固定源FM生成策略时，对角、重采样和独立运行估计器之间的差异在约2%以内，并且比全协方差估计低约10%，这一差距归因于协方差采样噪声。大的非对角协方差近似对称，在传播时大部分抵消，而不是像先前假设的那样小或为负。对于FM控制棒插值和组合策略（FM-CRd），keff与精确扰动参考值在60 pcm（约两个标准差）内匹配，裂变源在0.7%内匹配，而对角估计器和重采样估计器密切一致，并且保守约两倍。鉴于这一点以及全协方差的过高内存成本，推荐对角Delta方法作为实际默认选择，全协方差保留用于系统的单次表征。
英文摘要：
The fission matrix (FM) method recasts neutron transport in matrix form, enabling fast, interpolation-based reactor calculations from a pre-computed database of Monte Carlo-derived coefficients. Propagation of the underlying Monte Carlo statistical uncertainty to the FM eigenvalue and eigenvector is rarely rigorous: prior approaches assume independent coefficients without testing this against their actual covariance. This work derives a full-covariance Delta-method framework for propagating uncertainty to keff and the fission source, and evaluates it with two cheaper alternatives, a diagonal-covariance approximation and direct resampling of the FM coefficients, using an OpenMC model of the JSI TRIGA Mark-II reactor. For the all-rods-out case, these three estimators and an empirical benchmark of 100 independent Monte Carlo runs agree within 5.7% for keff and 1% for the fission source. The sign of the diagonal approximation's bias flips between the two statistics levels, so it must be checked case by case. With a global fixed-source FM generation strategy, the diagonal, resampling, and independent-run estimators agree within about 2% and lie roughly 10% below the full-covariance estimate, a gap attributed to covariance sampling noise. The large off-diagonal covariance is nearly symmetric and mostly cancels when propagated, rather than being small or negative as previously assumed. For the FM control-rod interpolation and combination strategy (FM-CRd), keff matches an exact perturbed reference within 60 pcm (about two standard deviations) and the fission source within 0.7%, while the diagonal and resampling estimators agree closely and are conservative by about a factor of two. Given this and the prohibitive memory cost of the full covariance, the diagonal Delta method is recommended as the practical default, with the full covariance reserved for one-time characterization of a system.
