Producing thousands of simulations of the dark matter distribution in the Universe with increasing precision is a challenging but critical task to facilitate the exploitation of current and forthcoming cosmological surveys. Many inexpensive substitutes to full $N$-body simulations have been proposed, even though they often fail to reproduce the statistics of the smaller, non-linear scales. Among these alternatives, a common approximation is represented by the lognormal distribution, which comes with its own limitations as well, while being extremely fast to compute even for high-resolution density fields. In this work, we train a generative deep learning model, mainly made of convolutional layers, to transform projected lognormal dark matter density fields to more realistic dark matter maps, as obtained from full $N$-body simulations. We detail the procedure that we follow to generate highly correlated pairs of lognormal and simulated maps, which we use as our training data, exploiting the information of the Fourier phases. We demonstrate the performance of our model comparing various statistical tests with different field resolutions, redshifts and cosmological parameters, proving its robustness and explaining its current limitations. When evaluated on 100 test maps, the augmented lognormal random fields reproduce the power spectrum up to wavenumbers of $1 \ h \ \rm{Mpc}^{-1}$, and the bispectrum within 10%, and always within the error bars, of the fiducial target simulations. Finally, we describe how we plan to integrate our proposed model with existing tools to yield more accurate spherical random fields for weak lensing analysis.

翻译：生成数千个精度持续提升的宇宙暗物质分布模拟，是促进当前及未来宇宙学巡天观测数据利用的关键挑战性任务。尽管全N体模拟的廉价替代方案已被广泛提出，但这些方法通常无法准确复现小尺度非线性区域的统计特征。在对数正态分布这一常用近似方法中，尽管其计算速度极快，甚至可处理高分辨密度场，但仍存在固有局限。本研究训练了主要由卷积层构成的生成式深度学习模型，将投影对数正态暗物质密度场转化为从全N体模拟获得的更真实暗物质分布图。我们详细阐述了生成高度相关对数正态图与模拟图对（作为训练数据）的流程，并利用傅里叶相位信息进行优化。通过对比不同场分辨率、红移及宇宙学参数下的多种统计检验，我们验证了模型的鲁棒性并解释了其当前局限性。在100张测试图上，增强后的对数正态随机场可在波数达$1 \ h \ \rm{Mpc}^{-1}$范围内复现功率谱，双谱误差在10%以内且始终处于基准目标模拟的误差棒内。最后，我们阐述了将该模型与现有工具集成以生成更精确弱透镜分析球面随机场的实施规划。