Deep generative models, such as Generative Adversarial Networks (GANs) or Variational Autoencoders (VAs) have been demonstrated to produce images of high visual quality. However, the existing hardware on which these models are trained severely limits the size of the images that can be generated. The rapid growth of high dimensional data in many fields of science therefore poses a significant challenge for generative models. In cosmology, the large-scale, three-dimensional matter distribution, modeled with N-body simulations, plays a crucial role in understanding the evolution of structures in the universe. As these simulations are computationally very expensive, GANs have recently generated interest as a possible method to emulate these datasets, but they have been, so far, mostly limited to two dimensional data. In this work, we introduce a new benchmark for the generation of three dimensional N-body simulations, in order to stimulate new ideas in the machine learning community and move closer to the practical use of generative models in cosmology. As a first benchmark result, we propose a scalable GAN approach for training a generator of N-body three-dimensional cubes. Our technique relies on two key building blocks, (i) splitting the generation of the high-dimensional data into smaller parts, and (ii) using a multi-scale approach that efficiently captures global image features that might otherwise be lost in the splitting process. We evaluate the performance of our model for the generation of N-body samples using various statistical measures commonly used in cosmology. Our results show that the proposed model produces samples of high visual quality, although the statistical analysis reveals that capturing rare features in the data poses significant problems for the generative models. We make the data, quality evaluation routines, and the proposed GAN architecture publicly available at https://github.com/nperraud/3DcosmoGAN.

中文翻译：

---

宇宙N体模拟：可扩展生成模型的挑战

深度生成模型，例如生成对抗网络（GAN）或变体自动编码器（VA），已被证明可以产生高视觉质量的图像。但是，在其上训练这些模型的现有硬件严重限制了可以生成的图像的大小。因此，在许多科学领域中，高维数据的快速增长对生成模型提出了重大挑战。在宇宙学中，以N体模拟为模型的大规模三维物质分布在理解宇宙中结构的演变中起着至关重要的作用。由于这些模拟在计算上非常昂贵，因此GAN最近引起了人们的兴趣，将其作为模拟这些数据集的一种可能方法，但到目前为止，它们大多仅限于二维数据。在这项工作中 我们引入了一个用于生成三维N体模拟的新基准，以激发机器学习社区中的新思想，并进一步接近宇宙学中生成模型的实际使用。作为第一个基准测试结果，我们提出了一种可扩展的GAN方法，用于训练N体三维立方体生成器。我们的技术依赖于两个关键的构建块，（i）将高维数据的生成划分为较小的部分，（ii）使用多尺度方法来有效捕获可能会在拆分过程中丢失的全局图像特征。我们使用宇宙学中常用的各种统计量度来评估我们模型产生N体样本的性能。我们的结果表明，提出的模型可产生高视觉质量的样本，尽管统计分析表明，捕获数据中的稀有特征对生成模型构成了重大问题。我们在https://github.com/nperraud/3DcosmoGAN上公开提供了数据，质量评估例程和提议的GAN架构。