用神经网络优化宇宙初始条件，突破非微分模拟的限制。
Learning the Universe: Learning to Optimize Cosmic Initial Conditions with Non-Differentiable Structure Formation Models
- 设计无需梯度的神经优化器，迭代搜索最佳初始条件。
- 在非线性区域（k~1h Mpc⁻¹）交叉相关率达80%以上。
- 适合需要高精度场级推断的宇宙学研究者使用。
下一代星系大尺度分布巡天需应对复杂非线性建模挑战，以挖掘小尺度上的丰富信息。场级推断提供了超越统计量的全新途径，可利用星系分布的全部信息。然而，当前方法常依赖包含非微分成分的数值模拟，阻碍了高效梯度驱动推断的应用。本文提出学习宇宙：通过学习优化（LULO），一种用于重建三维宇宙初始条件的无梯度框架。该方法将深度学习应用于训练优化算法，使最先进的非微分模拟器能在场级上拟合观测数据。关键在于，神经优化器仅作为迭代搜索工具，始终保留在物理模拟闭环中，确保可扩展性与可靠性。我们在仅含暗物质的N体模拟中，通过球对称密度算法识别出$M_{200 m{c}}$晕，成功重构初始条件。推导出的暗物质与晕密度场在非线性区域（k~1h Mpc⁻¹）与真实值的交叉相关率≥80%。额外宇宙学测试显示，功率谱、三阶相关函数、晕质量函数及速度均被准确恢复。本工作为超越可微分物理模型要求的非线性场级推断开辟了新路径。
原文摘要 · Abstract (English)
Making the most of next-generation galaxy clustering surveys requires overcoming challenges in complex, non-linear modelling to access the significant amount of information at smaller cosmological scales. Field-level inference has provided a unique opportunity beyond summary statistics to use all of the information of the galaxy distribution. However, addressing current challenges often necessitates numerical modelling that incorporates non-differentiable components, hindering the use of efficient gradient-based inference methods. In this paper, we introduce Learning the Universe by Learning to Optimize (LULO), a gradient-free framework for reconstructing the 3D cosmic initial conditions. Our approach advances deep learning to train an optimization algorithm capable of fitting state-of-the-art non-differentiable simulators to data at the field level. Importantly, the neural optimizer solely acts as a search engine in an iterative scheme, always maintaining full physics simulations in the loop, ensuring scalability and reliability. We demonstrate the method by accurately reconstructing initial conditions from $M_{200\mathrm{c}}$ halos identified in a dark matter-only $N$-body simulation with a spherical overdensity algorithm. The derived dark matter and halo overdensity fields exhibit $\geq80\%$ cross-correlation with the ground truth into the non-linear regime $k \sim 1h$ Mpc$^{-1}$. Additional cosmological tests reveal accurate recovery of the power spectra, bispectra, halo mass function, and velocities. With this work, we demonstrate a promising path forward to non-linear field-level inference surpassing the requirement of a differentiable physics model.
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