用快速神经网络重建宇宙初始物质分布，精度高且兼容主流模拟器。
Mean-Field Simulation-Based Inference for Cosmological Initial Conditions
- 将初始密度场后验设为傅里叶空间对角高斯，可训练均值与协方差。
- 训练仅需1小时，采样1000次低于3秒（128³分辨率）。
- 适用于不可微的N体模拟器，适合需要高效重建的宇宙学研究者。
从晚期观测中重建宇宙初始条件（ICs）是一项艰巨任务，依赖于计算成本高昂的模拟器和复杂的统计方法来处理数百万维参数空间。本文提出一种基于均场模拟的贝叶斯场重建方法：将初始物质密度场的后验分布建模为傅里叶空间中的对角高斯分布，其均值和协方差为可训练参数。训练时间约1小时（GPU），在128³分辨率下生成1000个样本耗时小于3秒。该方法支持行业标准的非可微N体模拟器，并通过汇总统计量验证了重构初始条件的保真度。
原文摘要 · Abstract (English)
Reconstructing cosmological initial conditions (ICs) from late-time observations is a difficult task, which relies on the use of computationally expensive simulators alongside sophisticated statistical methods to navigate multi-million dimensional parameter spaces. We present a simple method for Bayesian field reconstruction based on modeling the posterior distribution of the initial matter density field to be diagonal Gaussian in Fourier space, with its covariance and the mean estimator being the trainable parts of the algorithm. Training and sampling are extremely fast (training: $\sim 1 \, \mathrm{h}$ on a GPU, sampling: $\lesssim 3 \, \mathrm{s}$ for 1000 samples at resolution $128^3$), and our method supports industry-standard (non-differentiable) $N$-body simulators. We verify the fidelity of the obtained IC samples in terms of summary statistics.
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