通过自监督物理信息神经网络学习恒星结构方程
Learning the Stellar Structure Equations via Self-supervised Physics-Informed Neural Networks
AI总结：
本文提出一种自监督物理信息神经网络框架，用于无网格求解恒星结构方程，通过物理损失项强制满足结构方程，实现连续径向分布预测，验证结果表明其在大规模恒星合成中具有高效性和准确性。
摘要：
恒星天文学依赖于对恒星内部物理条件的准确描述。传统求解器如MESA（Modules for Experiments in Stellar Astrophysics）采用自适应有限差分方法，对于大规模恒星合成（>10^9颗恒星）计算成本高且难以扩展。本文提出一种自监督物理信息神经网络（PINN）框架，提供无网格且完全可微的求解方法。模型输入恒星边界条件（中心和表面）以及化学组成，通过物理损失项强制满足结构方程，学习连续径向分布。为纳入真实微观物理，引入辅助神经网络近似方程 of 状态和不透明度表作为局部热力学状态的平滑可微函数。这些代理替代传统表格输入，实现端到端训练。一旦训练完成，模型可在整个径向域内产生连续解，无需离散化或插值。验证结果表明，与基准MESA模型相比，平均相对绝对误差为3.06%，平均R²分数为99.98%。本文首次展示了在无数据情况下通过PINN求解恒星结构方程的可行性，为大规模、物理信息驱动的恒星内部模拟奠定了基础，并为未来向时间依赖恒星演化的扩展打开了大门。
英文摘要：
Stellar astrophysics relies critically on accurate descriptions of the physical conditions inside stars. Traditional solvers such as \texttt{MESA} (Modules for Experiments in Stellar Astrophysics), which employ adaptive finite-difference methods, can become computationally expensive and challenging to scale for large stellar population synthesis ($>10^9$ stars). In this work, we present an self-supervised physics-informed neural network (PINN) framework that provides a mesh-free and fully differentiable approach to solving the stellar structure equations under hydrostatic and thermal equilibrium. The model takes as input the stellar boundary conditions (at the center and surface) together with the chemical composition, and learns continuous radial profiles for mass $M_r(r)$, pressure $P(r)$, density $ρ(r)$, temperature $T(r)$, and luminosity $L_r(r)$ by enforcing the governing structure equations through physics-based loss terms. To incorporate realistic microphysics, we introduce auxiliary neural networks that approximate the equation of state and opacity tables as smooth, differentiable functions of the local thermodynamic state. These surrogates replace traditional tabulated inputs and enable end-to-end training. Once trained for a given star, the model produces continuous solutions across the entire radial domain without requiring discretization or interpolation. Validation against benchmark \texttt{MESA} models across a range of stellar masses yields a Mean Relative Absolute Error of $3.06\%$ and an average $R^2$ score of $99.98\%$. To our knowledge, this is the first demonstration that the stellar structure equations can be solved in a fully self-supervised and data-free fashion employing PINNs. This work establishes a foundation for scalable, physics-informed emulation of stellar interiors and opens the door to future extensions toward time-dependent stellar evolution.
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