Set Transformer 从恒星观测推断中子星状态方程
Set Transformer inference of the neutron star equation of state from stellar observations
- University of Coimbra（科英布拉大学）
- Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）
- INFN Sezione di Ferrara（费拉拉意大利国家核物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出置换不变的 Set Transformer，从无序中子星观测集合中学习恒星到密度的映射，重建状态方程，误差随观测数减少，且不确定性校准良好。
AI中文摘要：
我们开发了一种置换不变的 Set Transformer，用于从可变大小、无序的中子星（NS）观测集合中重建致密物质的状态方程（EoS）。该模型接收恒星质量以及半径、潮汐形变率或两者兼有，并在固定密度网格上预测压力 $P(n)$ 或声速 $c_s^2(n)$，同时给出依赖于密度的不确定性。架构中没有任何部分预先规定哪颗恒星提供哪个密度的信息：自注意力机制以非线性方式耦合所有观测，每个密度点通过其自身的可学习查询读取整个集合，因此恒星到密度的映射是从数据中学习得到的。在独立的逐段多方和 Gaussian-process EoS 系综上训练后，该模型提供了校准良好的预测，其不确定性在稳定恒星无法探测的密度区域增加。重建误差随观测数量增加而减小，而在固定观测数量下，潮汐形变率通常能提高精度，即使其本身带有测量噪声。敏感性分析揭示了密度局域映射：在压力模型中，密度 $n$ 处的预测最强烈依赖于中心密度接近 $n$ 的恒星。我们还表明，模型对推断出的恒星致密度的敏感性提供了最小中心密度的信息。这些结果表明，基于集合的神经推断（其中恒星到密度的映射是学习而非假设的）能够以校准的不确定性提取物理上可解释的 EoS 信息。
英文摘要：
We develop a permutation-invariant Set Transformer to reconstruct the equation of state (EoS) of dense matter from variable-size, unordered sets of neutron star (NS) observations. The model takes stellar masses together with radii, tidal deformabilities, or both, and predicts either the pressure $P(n)$ or the sound speed $c_s^2(n)$ on a fixed density grid, along with density-dependent uncertainties. Nothing in the architecture prescribes which star informs which density: self-attention couples all observations nonlinearly, and each density point reads the full set through its own learnable query, so the star-to-density mapping is learned from the data. Trained on independent piecewise-polytropic and Gaussian-process EoS ensembles, the model provides well-calibrated predictions whose uncertainty increases in density regions that stable stars cannot probe. Reconstruction errors decrease with the number of observations, while tidal deformability generally improves accuracy at a fixed observation count, even when it carries its own measurement noise. Sensitivity analysis reveals a density-local mapping: in the pressure models, predictions at density $n$ depend most strongly on stars whose central densities are near $n$. We also show that the sensitivity of the model to the inferred stellar compactness provides information on the minimum central density. These results demonstrate that set-based neural inference, in which the star-to-density mapping is learned rather than assumed, can extract physically interpretable EoS information with calibrated uncertainties.
