板几何中子输运序列加速方法的演化发现 (Evolutionary Discovery of Sequence Acceleration Methods for Slab Geometry Neutron Transport)

from arxiv, This work was presented at a special conference organized to honor Prof. Ganapol of University of Arizona on his retirement. It has been submitted to a follow-up nse publication call

We present a genetic programming approach to automatically discover convergence acceleration methods for discrete ordinates solutions of neutron transport problems in slab geometry. Classical acceleration methods such as Aitken's delta-squared and Wynn epsilon assume specific convergence patterns and do not generalize well to the broad set of transport problems encountered in practice. We evolved mathematical formulas specifically tailored to SN convergence characteristics in this work. The discovered accelerator, featuring second differences and cross-product terms, achieved over 75 percent success rate in improving convergence compared to raw sequences - almost double that observed for classical techniques for the problem set considered. This work demonstrates the potential for discovering novel numerical methods in computational physics via genetic programming and attempts to honor Prof. Ganapol's legacy of advancing experimental mathematics applied to neutron transport.

翻译：本文提出一种遗传编程方法，用于自动发现板几何中子输运问题离散纵坐标解的收敛加速方法。经典的加速方法如Aitken的delta平方法和Wynn epsilon法假设了特定的收敛模式，难以推广到实践中遇到的广泛输运问题。本研究演化出了专门针对SN收敛特性定制的数学公式。所发现的加速器具有二阶差分和交叉乘积项，与原始序列相比，在改善收敛性方面取得了超过75%的成功率——对于所考虑的问题集，这几乎是经典技术所观察到的成功率的两倍。这项工作展示了通过遗传编程在计算物理中发现新型数值方法的潜力，并试图致敬Ganapol教授在推进应用于中子输运的实验数学方面的遗产。