A primordial state of matter consisting of free quarks and gluons that existed in the early universe a few microseconds after the Big Bang is also expected to form in high-energy heavy-ion collisions. Determining the equation of state (EoS) of such a primordial matter is the ultimate goal of high-energy heavy-ion experiments. Here we use supervised learning with a deep convolutional neural network to identify the EoS employed in the relativistic hydrodynamic simulations of heavy ion collisions. High-level correlations of particle spectra in transverse momentum and azimuthal angle learned by the network act as an effective EoS-meter in deciphering the nature of the phase transition in quantum chromodynamics. Such EoS-meter is model-independent and insensitive to other simulation inputs including the initial conditions for hydrodynamic simulations.

We investigate with a transport approach the cold and hot nuclear matter effects on the charmonium transverse momentum distributions in relativistic heavy ion collisions. The newly defined nuclear modification factor $r_{AA}={\langle p_T^2\rangle }_{AA}/{\langle p_T^2\rangle }_{pp}$ and elliptic flow $v_2$ for $J/\psi$ are sensitive to the nature of the hot medium and the thermalization of heavy quarks. From Super Proton Synchrotron (SPS) through Relativistic Heavy Ion Collider (RHIC) to Large Hadron Collider (LHC) colliding energies, we observe dramatic changes in the centrality dependence of $r_{AA}$. We find that, at LHC energy, the finally observed charmonia are dominated by the regeneration from thermalized heavy quarks.

We explore the perspectives of machine learning techniques in the context of quantum field theories. In particular, we discuss two-dimensional complex scalar field theory at nonzero temperature and chemical potential—a theory with a nontrivial phase diagram. A neural network is successfully trained to recognize the different phases of this system and to predict the values of various observables, based on the field configurations. We analyze a broad range of chemical potentials and find that the network is robust and able to recognize patterns far away from the point where it was trained. Aside from the regressive analysis, which belongs to supervised learning, an unsupervised generative network is proposed to produce new quantum field configurations that follow a specific distribution. An implicit local constraint fulfilled by the physical configurations was found to be automatically captured by our generative model. We elaborate on potential uses of such a generative approach for sampling outside the training region.

Although seemingly disparate, high-energy nuclear physics (HENP) and machine learning (ML) have begun to merge in the last few years, yielding interesting results. It is worthy to raise the profile of utilizing this novel mindset from ML in HENP, to help interested readers see the breadth of activities around this intersection. The aim of this mini-review is to inform the community of the current status and present an overview of the application of ML to HENP. From different aspects and using examples, we examine how scientific questions involving HENP can be answered using ML.

Using deep convolutional neural network (CNN), the nature of the QCD transition can be identified from the final-state pion spectra from hybrid model simulations of heavy-ion collisions that combines a viscous hydrodynamic model with a hadronic cascade “after-burner”. Two different types of equations of state (EoS) of the medium are used in the hydrodynamic evolution. The resulting spectra in transverse momentum and azimuthal angle are used as the input data to train the neural network to distinguish different EoS. Different scenarios for the input data are studied and compared in a systematic way. A clear hierarchy is observed in the prediction accuracy when using the event-by-event, cascade-coarse-grained and event-fine-averaged spectra as input for the network, which are about 80%, 90% and 99%, respectively. A comparison with the prediction performance by deep neural network (DNN) with only the normalized pion transverse momentum spectra is also made. High-level features of pion spectra captured by a carefully-trained neural network were found to be able to distinguish the nature of the QCD transition even in a simulation scenario which is close to the experiments.