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利用场级模拟器从非线性宇宙结构中对初始条件进行贝叶斯推断

Bayesian Inference of Initial Conditions from Non-Linear Cosmic Structures using Field-Level Emulators

Ludvig Doeser, Drew Jamieson, Stephen Stopyra, Guilhem Lavaux, Florent Leclercq, Jens Jasche

备注：
19 pages, 15 figures. Updated to match version accepted by MNRAS (published 2024/11/27)
发表信息：
Monthly Notices of the Royal Astronomical Society, Volume 535, Issue 2, December 2024, Pages 1258-1277
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AI总结：

本研究在BORG贝叶斯推断算法中引入基于V-net的场级模拟器，结合N体模拟验证了其能高效准确重建宇宙初始条件，精确再现暗晕属性，为下一代宇宙学数据分析提供高效的非线性建模方案。

摘要：

分析下一代宇宙学数据需要在非线性引力结构形成的精确建模与计算需求之间取得平衡。我们提出了一种解决方案：在基于哈密顿蒙特卡洛的BORG（贝叶斯星系起源重建）推断算法中，引入一个基于机器学习的场级模拟器。该模拟器基于V-net神经网络架构构建，对一阶拉格朗日微扰理论的预测结果进行增强，使其与全N体模拟结果精确对齐，同时大幅缩短评估时间。我们基于N体模拟生成的非线性大尺度结构与高斯噪声构建模拟数据，测试了该模拟器集成到BORG中用于采样宇宙初始条件的效果。该方法能够高效且准确地探索初始条件的高维参数空间，完整提取分辨率为$1.95h^{-1}$ Mpc的分箱数据场的互相关信息。在高达奈奎斯特频率$k_\text{N} \approx 2.79h \\\\; \text{Mpc}^{-1}$的范围内，功率谱和双谱与真实值达到了百分比级别的一致性。后验重模拟——即利用推断出的初始条件进行N体模拟——表明，初始条件的信息恢复程度足以精确再现暗晕属性。具体而言，我们在$[0.853,16]\times 10^{14}M_{\odot}h^{-1}$的不同质量分箱中，得到了高度精确的$M_{200\text{c}}$暗晕质量函数和暗晕堆叠密度轮廓。由于所有可用的互相关信息都已被提取，我们确认初始条件恢复的局限性源于噪声水平和数据网格分辨率。这一结果颇具前景，因为它凸显了精确非线性建模的重要性，表明在更小尺度上提取额外信息具有潜力。

英文摘要：

Analysing next-generation cosmological data requires balancing accurate modeling of non-linear gravitational structure formation and computational demands. We propose a solution by introducing a machine learning-based field-level emulator, within the Hamiltonian Monte Carlo-based Bayesian Origin Reconstruction from Galaxies (BORG) inference algorithm. Built on a V-net neural network architecture, the emulator enhances the predictions by first-order Lagrangian perturbation theory to be accurately aligned with full $N$-body simulations while significantly reducing evaluation time. We test its incorporation in BORG for sampling cosmic initial conditions using mock data based on non-linear large-scale structures from $N$-body simulations and Gaussian noise. The method efficiently and accurately explores the high-dimensional parameter space of initial conditions, fully extracting the cross-correlation information of the data field binned at a resolution of $1.95h^{-1}$ Mpc. Percent-level agreement with the ground truth in the power spectrum and bispectrum is achieved up to the Nyquist frequency $k_\mathrm{N} \approx 2.79h \; \mathrm{Mpc}^{-1}$. Posterior resimulations - using the inferred initial conditions for $N$-body simulations - show that the recovery of information in the initial conditions is sufficient to accurately reproduce halo properties. In particular, we show highly accurate $M_{200\mathrm{c}}$ halo mass function and stacked density profiles of haloes in different mass bins $[0.853,16]\times 10^{14}M_{\odot}h^{-1}$. As all available cross-correlation information is extracted, we acknowledge that limitations in recovering the initial conditions stem from the noise level and data grid resolution. This is promising as it underscores the significance of accurate non-linear modeling, indicating the potential for extracting additional information at smaller scales.

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