用机器学习从数据中自动发现粒子散射的深层关系。
Learning the S-matrix from data: Rediscovering gravity from gauge theory via symbolic regression
- 用符号回归从数值数据中重构散射振幅结构。
- 五外腿以内高精度复现了KLT、KK、BCJ等关键关系。
- 适合对理论物理与数据驱动研究感兴趣的读者。
我们证明，现代机器学习方法可直接从数值的树图散射数据中自主重建若干标志性解析结构。特别地，通过将符号回归应用于以曼德尔施塔姆变量为输入特征的色序杨-米尔斯振幅，成功复现了基奥-刘-特耶（KLT）关系。结合标准特征选择技术（列主元QR分解），我们同时恢复了克莱斯-奎伊夫（KK）和伯恩-卡拉斯科-约翰逊（BCJ）关系，无需任何群论先验即可识别部分振幅的最小基。在五外腿以内，仅依赖极少理论先验，即实现了树图阶KLT关系的高数值精度。我们还讨论了该方法推广至更高多重性的挑战。结果表明，符号回归是探索散射振幅景观解析结构的实用工具，并提出一种通用的数据驱动策略来发现一般理论中的隐藏关系。作为对比，我们与近期提出的基于神经网络的方法进行了基准测试。
原文摘要 · Abstract (English)
We demonstrate that modern machine-learning methods can autonomously reconstruct several flagship analytic structures in scattering amplitudes directly from numerical on-shell data. In particular, we show that the Kawai--Lewellen--Tye (KLT) relations can be rediscovered using symbolic regression applied to colour-ordered Yang--Mills amplitudes with Mandelstam invariants as input features. Using standard feature-selection techniques, specifically column-pivoted QR factorisation, we simultaneously recover the Kleiss--Kuijf and Bern--Carrasco--Johansson (BCJ) relations, identifying a minimal basis of partial amplitudes without any group-theoretic input. We obtain the tree-level KLT relations with high numerical accuracy up to five external legs, using only minimal theoretical priors, and we comment on the obstacles to generalising the method to higher multiplicity. Our results establish symbolic regression as a practical tool for exploring the analytic structure of the scattering-amplitude landscape, and suggests a general data-driven strategy for uncovering hidden relations in general theories. For comparison, we benchmark this general approach with a recently introduced neural-network based method.
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