用机器学习挖掘费曼积分的奇异结构，揭示深层数学规律
Uncovering Singularities in Feynman Integrals via Machine Learning
- 基于符号回归构建可解释的机器学习框架
- 成功重构复杂费曼积分的完整符号字母表
- 适用于多圈振幅分析，适合理论物理研究者
我们提出一种基于符号回归的机器学习框架，用于提取多圈费曼积分的完整符号字母表。该方法聚焦于解析结构而非积分约化，具有广泛的适用性和可解释性，能在非平凡例子中成功重建完整的符号字母表，展现出鲁棒性与普遍性。不仅加速了具体计算，更实现了对解析结构的普遍揭示。该框架为多圈振幅分析开辟了新路径，提供了探索散射振幅的通用工具。
原文摘要 · Abstract (English)
We introduce a machine-learning framework based on symbolic regression to extract the full symbol alphabet of multi-loop Feynman integrals. By targeting the analytic structure rather than reduction, the method is broadly applicable and interpretable across different families of integrals. It successfully reconstructs complete symbol alphabets in nontrivial examples, demonstrating both robustness and generality. Beyond accelerating computations case by case, it uncovers the analytic structure universally. This framework opens new avenues for multi-loop amplitude analysis and provides a versatile tool for exploring scattering amplitudes.
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