AI 中文总结
该研究将机器学习与物理约束结合，用符号回归工具PySR推导三体系统通用有限体积外推公式，在短程、长程及中间力程均表现良好，为强子物理提供了传统方法无法得到的新解析结果。
AI 中文摘要
有限体积外推（FVE）是格点计算中提取物理可观测量的关键步骤。尽管两体和三体系统中短程势的严格FVE公式已成熟建立，但力程与格点尺寸L相当的长程相互作用仍具挑战性。我们扩展了此前针对两体系统的数据驱动方案，应用符号回归工具PySR来推导通用三体FVE公式。对于短程势，我们复现了两种极限情况，即κ₃≫κ₂和κ₃~κ₂；对于纯长程势，我们得到了专用解析表达式，结合短程贡献后，得到了与原始PySR解一致的统一公式，该公式在约1 fm的中间力程范围内表现优异。本研究表明，将机器学习与物理约束相结合可获得传统理论工具无法得到的新颖解析结果，推动了强子物理领域的数据驱动方法发展。
英文摘要
Finite-volume extrapolation (FVE) is essential for extracting physical observables in the lattice calculation. While rigorous FVE formulations are well established for short-range potentials in both two- and three-body systems, long-range interactions with force ranges comparable to the lattice size $L$ remain challenging. Extending a previous data-driven scheme for two-body systems, we apply symbolic regression (PySR) to uncover universal three-body FVE formulae. For short-range potentials, we reproduce the two limiting cases, i.e. $κ_3\ggκ_2$ and $κ_3\simκ_2$. For pure long-range potentials, we obtain a dedicated analytic expression, and after incorporating short-range contributions, we uncover a unified formula consistent with the original PySR solution, which performs excellently in the intermediate force range around 1 fm. This work demonstrates that combining machine learning with physical constraints can yield novel analytical results inaccessible to conventional theoretical tools, advancing data-driven methodologies in hadron physics.
Comments19 pages, 8 figures
