AI 中文总结
该研究用机器学习辅助重建银河系旋转曲线，利用73个观测数据点比较多种方法性能，岭回归表现最佳。将重建结果嵌入时空，通过爱因斯坦方程确定相关函数，验证能量条件等，为暗物质晕模型提供新方案，建立运动学与时空几何联系。
AI 中文摘要
我们提出了一种机器学习辅助的银河系旋转曲线分析重建方法，并在相对论时空背景下讨论其意义。利用0.1 - 95.56千秒差距范围内的73个观测数据点重建旋转曲线，比较了岭回归、套索回归和前馈神经网络的性能。岭回归预测最稳定，\(R^2 = 0.9824 ± 0.0064\)，均方根误差为3.75千米/秒，且保留分析可解释性。将重建的速度剖面嵌入静态、球对称时空，通过爱因斯坦方程确定红移函数和质量函数，验证了所有能量条件满足。该框架为传统暗物质晕模型提供了经统计验证、数据驱动的替代方案，建立了运动学可观测量与相对论时空几何之间的直接联系。
英文摘要
We propose a machine learning-assisted analytical reconstruction of the Milky Way rotation curve and discuss its implications in a relativistic spacetime context. The rotation curve is reconstructed using 73 observational data points over the range 0.1-95.56 kpc, and we compare the performances of Ridge regression, LASSO regression, and feed-forward neural networks using a physically motivated functional basis. Ridge regression yields the most stable prediction with R2 = 0.9824 +/- 0.0064 and RMSE = 3.75 km/s, while retaining analytical interpretability. We embed the reconstructed velocity profile into a static, spherically symmetric spacetime, enabling the determination of the redshift function and the mass function through Einstein's equations. We verify that all energy conditions are satisfied, the sound speed remains subluminal, the circular orbits are stable, and the gravitational energy is negative, confirming the attractive nature of gravity. This framework provides a statistically validated, data-driven alternative to conventional dark matter halo models and establishes a direct connection between kinematical observables and relativistic spacetime geometry.
