  A deep convolutional neural network (CNN) is developed to study symmetry
energy $E_{\rm sym}(\rho)$ effects by learning the mapping between the symmetry
energy and the two-dimensional (transverse momentum and rapidity) distributions
of protons and neutrons in heavy-ion collisions. Supervised training is
performed with labelled data-set from the ultrarelativistic quantum molecular
dynamics (UrQMD) model simulation. It is found that, by using proton spectra on
event-by-event basis as input, the accuracy for classifying the soft and stiff
$E_{\rm sym}(\rho)$ is about 60% due to large event-by-event fluctuations,
while by setting event-summed proton spectra as input, the classification
accuracy increases to 98%. The accuracy for 5-label (5 different $E_{\rm
sym}(\rho)$) classification task are about 58% and 72% by using proton and
neutron spectra, respectively. For the regression task, the mean absolute error
(MAE) which measures the average magnitude of the absolute differences between
the predicted and actual $L$ (the slope parameter of $E_{\rm sym}(\rho)$) are
about 20.4 and 14.8 MeV by using proton and neutron spectra, respectively.
Fingerprints of the density-dependent nuclear symmetry energy on the transverse
momentum and rapidity distributions of protons and neutrons can be identified
by convolutional neural network algorithm.

Nuclear Theory;Nuclear Experiment