  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.
