We train a neural network model to predict the full phase space evolution of cosmological N-body simulations. Its success implies that the neural network model is accurately approximating the Green's function expansion that relates the initial conditions of the simulations to its outcome at later times in the deeply nonlinear regime. We test the accuracy of this approximation by assessing its performance on well understood simple cases that have either known exact solutions or well understood expansions. These scenarios include spherical configurations, isolated plane waves, and two interacting plane waves: initial conditions that are very different from the Gaussian random fields used for training. We find our model generalizes well to these well understood scenarios, demonstrating that the networks have inferred general physical principles and learned the nonlinear mode couplings from the complex, random Gaussian training data. These tests also provide a useful diagnostic for finding the model's strengths and weaknesses, and identifying strategies for model improvement. We also test the model on initial conditions that contain only transverse modes, a family of modes that differ not only in their phases but also in their evolution from the longitudinal growing modes used in the training set. When the network encounters these initial conditions that are orthogonal to the training set, the model fails completely. In addition to these simple configurations, we evaluate the model's predictions for the density, displacement, and momentum power spectra with standard initial conditions for N-body simulations. We compare these summary statistics against N-body results and an approximate, fast simulation method called COLA. Our model achieves percent level accuracy at nonlinear scales of $k\sim 1\ \mathrm{Mpc}^{-1}\, h$, representing a significant improvement over COLA.
翻译:我们训练了一个神经网络模型来预测宇宙性N-体模拟的完整阶段空间演进。 它的成功意味着神经网络模型准确接近绿色的功能扩展, 将模拟的初始条件与深非线性系统后来的结果联系起来。 我们通过在已知精确解决方案或非常了解扩展的简单案例上评估其性能来测试这一近似的准确性。 这些假设包括球形配置、 孤立的平面波和两个互动的平面波: 初始条件与用于培训的高斯随机字段非常不同。 我们发现我们的神经网络模型非常接近于这些非常理解的情景, 表明这些网络已经从复杂的随机高斯培训数据中推导出一般物理原理并学习了非线性模式的组合。 这些测试还提供了一种有用的诊断, 用来查找模型的强弱之处, 并找出改进模型的战略。 我们还在初始条件上测试模型, 一种不仅在它们的各个阶段里,而且在其进化过程中, 也在它们与长期增长的A- 准确性统计中, 在初步的模型上, 这些模型中, 代表了我们用来进行模拟的快速预测的模型, 当我们接触到这些模型时, 这些模型的精确度, 当我们接触到这些模型时, 当我们使用了这些模型时, 在初步的精确的模型中, 当我们接触到这些模型中, 当我们使用了。