Spinodal Dataset for classification

The \textit{spinodal} dataset is a simulated dataset, created to identify the effects of a non-equilibrium deconfinement phase transition in relativistic nuclear collisions. The underlying physical question is to understand the non-perturbative interactions of the strong interaction in the high baryon density regime. These questions are closely related to the understanding of the deconfinement mechanism and consequently the dynamical generation of mass in Quantum Chromo Dynamics (QCD). To uncover the properties of dense and hot nuclear matter, the Compressed Baryonic Matter (CBM) experiment is under construction at the FAIR (Facility for Anti-proton and Ion Research) at GSI Darmstadt.
At FAIR, heavy nuclei (mostly lead and/or uranium) are accelerated to beam energies of several GeV per nucleon and brought to collision with a similar target at the CBM experiment. In this way, the nuclear matter is simultaneously heated and compressed, and since large nuclei are used, for a very short time, an equilibrated system of QCD matter at several times the nuclear saturation density and temperatures of up to 100~MeV is created. The dynamics that govern this system are determined by the strong interaction, i.e. QCD. Since the dynamic many–body problem of QCD cannot be solved explicitly nor numerically, our understanding of the matter created is based on interpretations of the collected data. This interpretation is done by comparing sophisticated model simulations, either based on relativistic fluid dynamics or microscopic transport simulations, with experimental observations.  
The presented dataset is the result of such a model simulation, based on a fluid dynamical simulation of heavy ion collisions in the presence of a first-order deconfinement phase transition. In particular, the dataset was created using two distinct scenarios, one where spinodal decomposition occurs and one where it does not. Spinodal decomposition is a well-known effect that describes the dynamics of phase separation and leads to the exponential growth of density fluctuations.  It is now of particular interest how these density fluctuations influence the observable final particle spectra as measured by the CBM experiment. In addition, since even the theoretical background of these fluctuations in the fast-expanding and small collision systems is not well understood, it is even of interest to understand whether all events will show such signals or they only occur on rare occasions. Thus, the application of machine learning methods to possibly uncover the effects of the QCD phase transition measured momentum spectra is of great interest.
The task for this effort is to identify those events which have undergone spinodal decomposition. In addition, for the physical interpretation, it is also important to see what a characteristic spinodal event looks like compared to a non-spinodal event. Finally, it is important to achieve high accuracy to see whether all events, simulated as spinodal events, also can be identified as such or if not every event shows the relevant characteristics.
To create the spinodal classification dataset, 27,000 central collision events of lead on lead are generated at a (typical FAIR/GSI) beam energy of $E_{\mathrm{lab}}=3.5\, A$~GeV, for each scenario: spinodal or not. From each event an 'image' is then generated, containing information on the net baryon density distribution in the transverse spatial $X-Y$ plane. This corresponds then to a 20-by-20 pixel histogram. We renormalized the pictures by their maximum bin value for each event separately, to avoid possible artifacts from one class having a larger density. The histograms are then flattened to a 400-column array-list of events.

The dataset was created as described in:

J.~Steinheimer, L.~Pang, K.~Zhou, V.~Koch, J.~Randrup and H.~Stoecker,
%``A machine learning study to identify spinodal clumping in high energy nuclear collisions,''
JHEP \textbf{12}, 122 (2019)

It was also used in:

L.~Benato, E.~Buhmann, M.~Erdmann, P.~Fackeldey, J.~Glombitza, N.~Hartmann, G.~Kasieczka, W.~Korcari, T.~Kuhr and J.~Steinheimer, \textit{et al.}
%``Shared Data and Algorithms for Deep Learning in Fundamental Physics,''
[arXiv:2107.00656 [cs.LG]].