相对论第一性原理驱动下的状态方程神经网络构建
Neural Network Construction of the Equation of State from Relativistic ab initio Calculations
陈康敏 1曲晓英 2童辉 3王锶博 4于阳阳2
作者信息
- 1. 厦门大学物理科学与技术学院，厦门 361001;贵州民族大学物理与机电工程学院，贵阳 550025
- 2. 贵州民族大学物理与机电工程学院，贵阳 550025
- 3. 中国原子能科学研究院，北京 102413;波恩大学赫尔姆霍兹辐射与核物理研究所及贝特理论物理中心，德国波恩 D-53115
- 4. 东京大学理学系研究科物理学专攻，日本东京 113-0033;重庆大学物理学院及重庆强耦合物理重点实验室，重庆 401331
- 折叠
摘要
在核物理和核天体物理中，约束超出饱和密度的核物质状态方程（EOS）具有至关重要的意义。 相对论~Brueckner-Hartree-Fock（RBHF）理论是一种基于现实核力的非微扰核多体方法，但其当前适用的最高密度范围仅限于约三倍饱和密度 $3\rho_0$ ($\rho_0=0.16\ \text{fm}^{-3}$)，因此需要借助可靠的外推技术扩展至更高密度区域。 本工作采用监督式机器学习方法，在低密度RBHF数据上训练了数千个神经网络。 通过施加热力学稳定性和光滑性约束，我们筛选出~264 个采用~Swish 激活函数的最优模型。 利用这些模型将~EOS 外推至高密度区间，获得了核物质对称能，进而计算了中子星的质量-半径关系和潮汐形变，所得结果与当前天文观测高度吻合。 外推不确定性通过统计系综方法进行量化，得到五倍饱和密度处的对称能~$E_\mathrm{sym}(5\rho_0)=136.0 \pm 52.8$~MeV，压强~$P(5\rho_0)=346.3 \pm 97.4~\mathrm{MeV/fm^3}$，最大中子星质量$M_\mathrm{max}=2.18 \pm 0.18~M_\odot$，以及潮汐形变~$\Lambda_{1.4M_\odot}=532 \pm 34$。 本工作建立了一个通用的数据驱动框架，将第一性原理计算与现代机器学习技术相结合，用于探索纯核子、无相变条件下的高密度外推。
Abstract
Constraining the nuclear matter equation of state (EOS) beyond saturation density is crucial in nuclear physics and astrophysics. While the relativistic Brueckner-Hartree-Fock (RBHF) theory, an \textit{ab initio} non-perturbative nuclear many-body theory starting from realistic interactions, accurately describes nuclear matter properties near the saturation density $\rho_0 \approx 0.16$~fm$^{-3}$, its applicability is limited to densities up to $3\rho_0$, necessitating a reliable extrapolation to higher densities. In this work, we employ supervised machine learning to train thousands of neural networks on low-density RBHF data. By enforcing thermodynamic consistency and smoothness, we select a subset of 264 optimal models employing the Swish activation function, which we identify as the most reliable choice for stable extrapolation after extensive testing and comparison. Using these models to extend the EOS to high density, we obtain the nuclear matter symmetry energy and then compute the neutron star mass-radius relation and tidal deformability, consistent with current astronomical observations. The corresponding extrapolation uncertainty originates from the combined contributions of both the 264 optimal models and the linear regression on nuclear matter EOS, yielding a symmetry energy of $E_\mathrm{sym}(5\rho_0)=136.0 \pm 52.8$~MeV, a pressure of $P(5\rho_0)=346.3 \pm 97.4~\mathrm{MeV/fm^3}$, a maximum neutron star mass of $M_\mathrm{max}=2.18 \pm 0.18~M_\odot$, and a tidal deformability of $\Lambda_{1.4M_\odot}=532 \pm 34$. This work establishes a general and data-driven framework to explore dense matter EOS under pure nucleons and non-phase-transition conditions by integrating \textit{ab initio} calculations with modern machine learning techniques.关键词
状态方程/相对论 Brueckner-Hartree-Fock/神经网络/中子星/对称能Key words
equation of state/relativistic Brueckner-Hartree-Fock/neural networks/neutron star/symmetry energy引用本文复制引用
陈康敏,曲晓英,童辉,王锶博,于阳阳.相对论第一性原理驱动下的状态方程神经网络构建[EB/OL].(2026-10-24)[2026-10-26].https://chinaxiv.org/abs/202610.00192.学科分类
天文学
