  Many random growth models have the property that the set of discovered sites,
scaled properly, converges to some deterministic set as time grows. Such
results are known as shape theorems. Typically, not much is known about the
shapes. For first passage percolation on $\mathbb{Z}^d$ we only know that the
shape is convex, compact, and inherits all the symmetries of $\mathbb{Z}^d$.
Using simulated data we construct and fit a neural network able to adequately
predict the shape of the set of discovered sites from the mean, standard
deviation, and percentiles of the distribution of the passage times. The
purpose of the note is two-fold. The main purpose is to give researchers a new
tool for \textit{quickly} getting an impression of the shape from the
distribution of the passage times -- instead of having to wait some time for
the simulations to run, as is the only available way today. The second purpose
of the note is simply to introduce modern machine learning methods into this
area of discrete probability, and a hope that it stimulates further research.
