用符号回归加速超标准模型物理研究，提升参数拟合效率
Symbolic Regression and Differentiable Fits in Beyond the Standard Model Physics
- 用符号回归构建可观测量与输入参数的显式表达式
- 对希格斯质量、暗物质密度等三类观测结果拟合精度高
- 相比神经网络更鲁棒，适合全局参数搜索
我们展示了符号回归（SR）在探测超标准模型（BSM）粒子物理中的有效性，以约束最小超对称标准模型（CMSSM）为例。该模型有四个任意参数，决定实验信号和宇宙学观测如暗物质遗迹密度。通过建立可观测量与输入参数间的符号表达式，可大幅加速现象学分析。本文聚焦希格斯质量、冷暗物质遗迹密度及μ子反常磁矩贡献。结果表明，符号回归能生成高度精确的解析表达式，并用于全局拟合，获得与传统方法一致的后验概率分布。此外，其关键优势在于可使用可微分方法进行拟合，而非依赖采样。与神经网络回归相比，符号回归在数据分布更广时表现更稳定，而神经网络需集中在有利区域的数据才能达到相当性能。
原文摘要 · Abstract (English)
We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of BSM physics this model has a number (four) of arbitrary parameters, which determine the experimental signals, and cosmological observables such as the dark matter relic density. We show that analysis of the phenomenology can be greatly accelerated by using symbolic expressions derived for the observables in terms of the input parameters. Here we focus on the Higgs mass, the cold dark matter relic density, and the contribution to the anomalous magnetic moment of the muon. We find that SR can produce remarkably accurate expressions. Using them we make global fits to derive the posterior probability densities of the CMSSM input parameters which are in good agreement with those performed using conventional methods. Moreover, we demonstrate a major advantage of SR which is the ability to make fits using differentiable methods rather than sampling methods. We also compare the method with neural network (NN) regression. SR produces more globally robust results, while NNs require data that is focussed on the promising regions in order to be equally performant.
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