Evolutionary Discovery of Sequence Acceleration Methods for Slab Geometry Neutron Transport

TL;DR

This paper uses genetic programming to automatically discover new convergence acceleration methods for neutron transport equations in slab geometry, outperforming classical techniques.

Contribution

It introduces a novel genetic programming approach to tailor convergence accelerators for neutron transport problems, achieving higher success rates than classical methods.

Findings

Achieved over 75% success rate in improving convergence

Discovered accelerators with second differences and cross-product terms

Nearly doubled effectiveness compared to classical techniques

Abstract

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.