AI 中文总结
研究利用函数展开计数预测蒙特卡罗输运循环间相关性，通过二维散射链基准比较传统与伽辽金降阶模型，降阶模型无需构建大矩阵估计积分自相关时间，余弦基收敛快，降基方法成本低偏差小，为相关计算提供有效途径。
AI 中文摘要
我们研究函数展开计数作为预测蒙特卡罗输运中循环间相关性的降基表示。使用具有反射边界的解析二维各向同性散射链基准，我们将传统离散单元马尔可夫链估计器与直接从基函数乘积的蒙特卡罗计数构建的伽辽金降阶模型进行比较。该降阶模型无需先构建大型离散转移矩阵即可估计积分自相关时间。对于基准问题，余弦基迅速收敛到精确结果，而多项式基随阶数增加呈现系统收敛。与离散分箱相比，降基方法在可比或更低求解成本下实现更低偏差，表明函数展开表示可为蒙特卡罗临界计算中的相关性预测、不确定性量化及未来方差减少方法提供有效途径。
英文摘要
We investigate functional expansion tallies as a reduced-basis representation for predicting inter-cycle correlations in Monte Carlo transport. Using an analytic two-dimensional isotropic scattering-chain benchmark with reflective boundaries, we compare a conventional discrete-cell Markov-chain estimator with a Galerkin reduced-order model built directly from Monte Carlo tallies of basis-function products. The reduced model estimates integrated autocorrelation time without first constructing a large discrete transition matrix. For the benchmark problem, the cosine basis converges rapidly to the exact result, while polynomial bases show systematic convergence with increasing order. Compared with discrete binning, the reduced-basis approach achieves lower bias at comparable or lower solve cost, suggesting that functional-expansion representations can provide an efficient path toward correlation prediction, uncertainty quantification, and future variance-reduction methods in Monte Carlo criticality calculations.
Comments4 pages, 4 figures, submitted to 2026 ANS Annual Conference
