基于欧拉和拉格朗日单圈微扰理论的星系功率谱快速精确可微代码
Fast and accurate differentiable code of the galaxy power spectrum based on Eulerian and Lagrangian one-loop perturbation theories
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中文总结 AI 辅助
本文提出基于JAX的星系功率谱单圈自动可微代码，支持欧拉和拉格朗日微扰理论，实现毫秒级GPU计算和0.01%精度，为首个LPT自动可微实现，适用于参数推断和原初特征研究。
中文摘要 AI 辅助
本文介绍了一个基于JAX-Python的星系功率谱实现，该实现达到有效场论大尺度结构中单圈阶精度，同时基于欧拉和拉格朗日微扰理论。代码利用JAX实现相对于宇宙学参数、星系偏置或反项系数等参数的自动微分。这促进了利用后验梯度进行参数推断的应用，例如哈密顿蒙特卡洛采样。代码在即时编译后，可在GPU上于几毫秒内计算EPT和LPT功率谱。我们还识别了与离散化相关的各种数值误差来源，并设计数值实现以最小化这些误差，与暴力数值积分相比，在尺度$k \lesssim 1\\, h\\, \mathrm{Mpc}^{-1}$上实现约$0.01\\%$的相对误差。值得注意的是，这是首个基于LPT的单圈星系功率谱自动可微实现。LPT中长波长位移的自然重求和进一步使代码非常适合涉及标准BAO特征之外的功率谱特征的应用，包括原初特征。我们的代码elf已公开可用。
英文摘要
This paper presents a JAX-Python implementation of the galaxy power spectrum up to one-loop order in the effective field theory of large-scale structure, based on both the Eulerian and Lagrangian perturbation theories. The code uses JAX to enable automatic differentiation with respect to parameters such as cosmology, galaxy bias, or counterterm coefficients. This facilitates applications such as parameter inference using the gradient of the posterior, e.g., Hamiltonian Monte Carlo sampling. The code can compute both the EPT and LPT power spectra in a few milliseconds on a GPU, after just-in-time compilation. We also identify the various sources of numerical errors associated with discretization, and design the numerical implementation to minimize them, achieving relative errors of order $0.01\%$ at scales $k \lesssim 1\, h\, \mathrm{Mpc}^{-1}$, compared with brute-force numerical integration. Notably, this is the first auto-differentiable implementation of the one-loop galaxy power spectrum based on LPT. The natural resummation of the long-wavelength displacements in LPT further makes the code well suited for applications involving features in the power spectrum beyond the standard BAO feature, including primordial features. Our code, elf, is publicly available.
发表机构
- Kyoto Sangyo University（京都产业大学）
- High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）
机构由 AI 辅助整理，请以论文原文为准。
