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.

翻译：充分利用下一代星系聚类巡天数据，需要克服复杂非线性建模的挑战，以获取更小宇宙尺度上的重要信息。场级推断提供了超越统计摘要的独特机遇，能够利用星系分布的全部信息。然而，解决当前挑战通常需要包含不可微分组件的数值建模，这阻碍了高效基于梯度的推断方法的应用。本文提出"通过优化学习宇宙"框架，这是一种用于重建三维宇宙初始条件的无梯度方法。我们的研究通过深度学习训练优化算法，使其能够将最先进的不可微分模拟器与场级观测数据进行拟合。值得注意的是，神经优化器仅作为迭代方案中的搜索引擎，始终保持完整物理模拟的闭环，确保方法的可扩展性和可靠性。我们通过精确重建暗物质专用N体模拟中采用球状过密度算法识别的$M_{200\mathrm{c}}$晕团的初始条件，验证了该方法的有效性。推导出的暗物质和晕团过密度场与真实情况在非线性区域$k \sim 1h$ Mpc$^{-1}$内保持$\geq80\%$的互相关性。额外的宇宙学测试显示，该方法能准确恢复功率谱、双谱、晕团质量函数和速度场分布。本研究表明，超越可微分物理模型要求的非线性场级推断具有可行的发展路径。