  We apply machine learning to the problem of finding numerical Calabi-Yau
metrics. Building on Donaldson's algorithm for calculating balanced metrics on
K\"ahler manifolds, we combine conventional curve fitting and machine-learning
techniques to numerically approximate Ricci-flat metrics. We show that machine
learning is able to predict the Calabi-Yau metric and quantities associated
with it, such as its determinant, having seen only a small sample of training
data. Using this in conjunction with a straightforward curve fitting routine,
we demonstrate that it is possible to find highly accurate numerical metrics
much more quickly than by using Donaldson's algorithm alone, with our new
machine-learning algorithm decreasing the time required by between one and two
orders of magnitude.
