用符号模型加速宇宙学计算，精度不降还更快
Symbolic Emulators for Cosmology: Accelerating Cosmological Analyses Without Sacrificing Precision
- 用符号近似替代数值计算，提升速度与内存效率
- 红移和Ωm范围全覆盖，精度达0.001%以上
- 适合需快速迭代的宇宙学参数分析任务
在宇宙学中，模拟器通过快速准确预测复杂物理模型，在高维参数空间探索中发挥关键作用，避免直接数值模拟带来的计算瓶颈。符号模拟器作为新兴方案，可在保持相当精度的同时显著加快计算速度。此前符号模拟器仅适用于较窄参数范围，本文将其扩展至当前宇宙学分析相关参数空间。针对ΛCDM模型中的超几何函数，我们提出了用于共动距离和线性增长因子的近似方法，对所有红移及Ω_{\rm m} ∈ [0.1, 0.5] 范围内，精度分别优于0.001%和0.05%。我们将符号模拟器集成至类似暗能量调查（Dark Energy Survey）的3×2pt分析中，结果与标准数值方法一致。符号模拟器在速度与内存占用上均有显著提升，展现出其在可扩展似然推断中的实际潜力。
原文摘要 · Abstract (English)
In cosmology, emulators play a crucial role by providing fast and accurate predictions of complex physical models, enabling efficient exploration of high-dimensional parameter spaces that would be computationally prohibitive with direct numerical simulations. Symbolic emulators have emerged as promising alternatives to numerical approaches, delivering comparable accuracy with significantly faster evaluation times. While previous symbolic emulators were limited to relatively narrow prior ranges, we expand these to cover the parameter space relevant for current cosmological analyses. We introduce approximations to hypergeometric functions used for the $Λ$CDM comoving distance and linear growth factor which are accurate to better than 0.001% and 0.05%, respectively, for all redshifts and for $Ω_{\rm m} \in [0.1, 0.5]$. We show that integrating symbolic emulators into a Dark Energy Survey-like $3\times2$pt analysis produces cosmological constraints consistent with those obtained using standard numerical methods. Our symbolic emulators offer substantial improvements in speed and memory usage, demonstrating their practical potential for scalable, likelihood-based inference.
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