用机器学习优化费曼积分归约的启发式策略，提升计算效率。
Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning
- 采用大语言模型生成代码的遗传编程方法探索新启发式规则。
- 成功复现现有最优启发式策略，并在某案例中实现小幅性能提升。
- 适合高能物理与引力波理论计算研究者参考使用。
费曼积分的逐项积分归约在现代理论粒子物理与引力波物理计算中常成为瓶颈，其性能高度依赖于启发式选择积分恒等式的方法。本文研究利用机器学习技术寻找更优的启发式策略。我们采用FunSearch——一种基于大型语言模型代码生成的遗传编程变体，探索可能的解决方案，随后使用强类型遗传编程精炼出有效策略。两种方法均成功复现了近期集成至积分归约求解器中的最先进启发式方法，并在一个实例中实现了对当前最优策略的小幅改进。
原文摘要 · Abstract (English)
Integration-by-parts reductions of Feynman integrals pose a frequent bottle-neck in state-of-the-art calculations in theoretical particle and gravitational-wave physics, and rely on heuristic approaches for selecting integration-by-parts identities, whose quality heavily influences the performance. In this paper, we investigate the use of machine-learning techniques to find improved heuristics. We use funsearch, a genetic programming variant based on code generation by a Large Language Model, in order to explore possible approaches, then use strongly typed genetic programming to zero in on useful solutions. Both approaches manage to re-discover the state-of-the-art heuristics recently incorporated into integration-by-parts solvers, and in one example find a small advance on this state of the art.
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