  We train a deep convolutional neural network to predict hydrodynamic results
for flow coefficients, average transverse momenta and charged particle
multiplicities in ultrarelativistic heavy-ion collisions from the initial
energy density profiles. We show that the neural network can be trained
accurately enough so that it can reliably predict the hydrodynamic results for
the flow coefficients and, remarkably, also their correlations like normalized
symmetric cumulants, mixed harmonic cumulants and flow-transverse-momentum
correlations. At the same time the required computational time decreases by
several orders of magnitude. To demonstrate the advantage of the significantly
reduced computation time, we generate 10M initial energy density profiles from
which we predict the flow observables using the neural network, which is
trained using 5k, and validated using 90k events per collision energy. We then
show that increasing the number of collision events from 90k to 10M can have
significant effects on certain statistics-expensive flow correlations, which
should be taken into account when using these correlators as constraints in the
determination of the QCD matter properties.
