Machine-learning-based identification for initial clustering structure in relativistic heavy-ion collisions

$\alpha$-clustering structure is a significant topic in light nuclei. A Bayesian convolutional neural network (BCNN) is applied to classify initial nonclustered and clustered configurations, namely Woods-Saxon distribution and three-$\alpha$ triangular (four-$\alpha$ tetrahedral) structure for ${}^{12}\mathrm{C}$ $\left({}^{16}\mathrm{O}\right)$, from heavy-ion collision events generated within a multiphase transport (AMPT) model. Azimuthal angle and transverse momentum distributions of charged pions are taken as inputs to train the classifier. On a multiple-event basis, the overall classification accuracy can reach $95\%$ for ${}^{12}\mathrm{C}/{}^{16}\mathrm{O}+{}^{197}\mathrm{Au}$ events at $\sqrt{S_{NN}}=200\mathrm{GeV}$. With proper constructions of samples, the predicted deviations on mixed samples with different proportions of both configurations could be within $5\%$. In addition, setting a simple confidence threshold can further improve the predictions on the mixed dataset. Our results indicate promising and extensive possibilities of application of machine-learning-based techniques to real data and some other problems in physics of heavy-ion collisions.

Figure 1

Nucleon distributions in the transverse plane for clustered ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ from 10000 events.

Figure 2

Two-dimensional azimuthal angle and transverse momentum distributions of charged pions for nonclustered and clustered ${}^{12}\mathrm{C}$ from a single AMPT-generated ${}^{12}\mathrm{C}+{}^{197}\mathrm{Au}$ collision event at $\sqrt{S_{NN}}=200\mathrm{GeV}$.

Figure 3

Same as Fig. 2 but for 4000 merged events which are rotated according to the event-by-event third-order participant plane.

Figure 4

Evolution of the validation accuracy during the training process for the dataset of two colliding systems ${}^{12}\mathrm{C}/{}^{16}\mathrm{O}+{}^{197}\mathrm{Au}$ with $N_{\mathrm{Event}}=1000$, 2000, and 4000.

Figure 5

The upper panels show the reliability diagrams for ${}^{12}\mathrm{C}$ with $N_{\mathrm{Event}}=4000$, ${}^{16}\mathrm{O}$ with $N_{\mathrm{Event}}=2000$, and ${}^{16}\mathrm{O}$ with $N_{\mathrm{Event}}=4000$. The lower panels show the sample fractions in each confidence bin.

Figure 6

Histograms of predictions on mixed samples for ${}^{12}\mathrm{C}$ with $N_{\mathrm{Event}}=4000$ (upper panels), ${}^{16}\mathrm{O}$ with $N_{\mathrm{Event}}=2000$ (middle panels), and ${}^{16}\mathrm{O}$ with $N_{\mathrm{Event}}=4000$ (lower panels) with different mixing proportions of the Woods-Saxon configuration.

Figure 7

Same as Fig. 6 but with a confidence threshold of 0.99.

Figure 8

Histograms of “measurements” based on all mixed samples for ${}^{12}\mathrm{C}$ with $N_{\mathrm{Event}}=4000$ (upper panels), ${}^{16}\mathrm{O}$ with $N_{\mathrm{Event}}=2000$ (middle panels), and ${}^{16}\mathrm{O}$ with $N_{\mathrm{Event}}=4000$ (lower panels) with different mixing proportions of the Woods-Saxon configuration.

Figure 9

Same as Fig. 8 but with a confidence threshold of 0.999.

Figure 10

Predicted proportion of the Woods-Saxon configuration versus true proportion of the Woods-Saxon configuration with different predicted times ($N_{\mathrm{Pred}}$) and amounts of mixed samples ($N_{\mathrm{Sample}}$). Here we take ${}^{12}\mathrm{C}$ with $N_{\mathrm{Event}}=4000$ as an example. The deviation along the $x$ axis is for clarity.

Figure 11

Histograms of predictions on the validation set from a regression model for ${}^{12}\mathrm{C}$ with $N_{\mathrm{Event}}=4000$.