We propose a method to explore the flavor structure of quarks and leptons with reinforcement learning. As a concrete model, we utilize a basic value-based algorithm for models with $U(1)$ flavor symmetry. By training neural networks on the $U(1)$ charges of quarks and leptons, the agent finds 21 models to be consistent with experimentally measured masses and mixing angles of quarks and leptons. In particular, an intrinsic value of normal ordering tends to be larger than that of inverted ordering, and the normal ordering is well fitted with the current experimental data in contrast to the inverted ordering. A specific value of effective mass for the neutrinoless double beta decay and a sizable leptonic CP violation induced by an angular component of flavon field are predicted by autonomous behavior of the agent. Our finding results indicate that the reinforcement learning can be a new method for understanding the flavor structure.

翻译：我们提出了一种利用强化学习探索夸克和轻子味结构的方法。作为具体模型，我们采用一种基于值函数的基础算法，用于具有$U(1)$味对称性的模型。通过训练神经网络处理夸克和轻子的$U(1)$荷，该智能体找到了21个与实验测量的夸克和轻子质量及混合角一致的模型。特别地，正常顺序的内在价值倾向于大于倒置顺序，且与倒置顺序相比，正常顺序能更好地拟合当前实验数据。智能体的自主行为预测了无中微子双β衰变的有效质量的具体数值，以及由flavon场角度分量引起的显著轻子CP破坏。我们的发现表明，强化学习可以成为理解味结构的一种新方法。