title: ÐÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ ÑÐµÐ½ÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÐ¸ Ð² ÑÑÐ¾Ð»ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸ÑÑ ÑÐ»ÑÑÑÐ°ÑÐµÐ»ÑÑÐ¸Ð²Ð¸ÑÑÑÐºÐ¸Ñ ÑÐ´ÐµÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Calculation of centrality in collisions of ultrarelativistic nuclei using machine learning methods
Creators: name: Ð¡Ð¸Ð½ÑÐ³Ð¸Ð½, Ð¡ÐµÑÐ³ÐµÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: ÑÐµÐ½ÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑ
ÑÐ»ÑÑÑÐ°ÑÐµÐ»ÑÑÐ¸Ð²Ð¸ÑÑÑÐºÐ¸Ðµ ÑÑÐ¾Ð»ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ñ
Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ðµ Ð¾Ð±ÑÑÐµÐ½Ð¸Ðµ
Ð¿Ð¾Ð»Ð¸Ð½Ð¾Ð¼Ð¸Ð°Ð»ÑÐ½Ð°Ñ ÑÐµÐ³ÑÐµÑÑÐ¸Ñ
centrality
ultrarelativistic collisions
machine learning
polynomial regression
pythia

description: ÐÐ´Ð½Ð¾Ð¹ Ð¸Ð· ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸Ðº ÑÑÐ¾Ð»ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ð¹ ÑÐ´ÐµÑ ÑÐ²Ð»ÑÐµÑÑÑ ÑÐµÐ½ÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑ ÑÐ¾Ð±ÑÑÐ¸Ñ, Ð¾ÑÑÐ°Ð¶Ð°ÑÑÐ°Ñ ÑÑÐµÐ¿ÐµÐ½Ñ Ð¿ÐµÑÐµÐºÑÑÑÐ¸Ñ Ð¼ÐµÐ¶Ð´Ñ Ð´Ð²ÑÐ¼Ñ ÑÑÐ°Ð»ÐºÐ¸Ð²Ð°ÑÑÐ¸Ð¼Ð¸ÑÑ ÑÐ´ÑÐ°Ð¼Ð¸. ÐÐ½Ð¾Ð¶ÐµÑÑÐ²ÐµÐ½Ð½Ð¾ÑÑÑ Ð·Ð°ÑÑÐ¶ÐµÐ½Ð½ÑÑ ÑÐ°ÑÑÐ¸Ñ Ð¸ ÑÐ¸ÑÐ»Ð¾ Ð½ÐµÐ¹ÑÑÐ¾Ð½Ð¾Ð², ÑÐ¾Ð¶Ð´Ð°ÑÑÐ¸ÑÑÑ Ð²Ð¾ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ð¸, ÑÑÐ²ÑÑÐ²Ð¸ÑÐµÐ»ÑÐ½Ñ Ðº Ð²ÐµÐ»Ð¸ÑÐ¸Ð½Ðµ ÑÐµÐ½ÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÐ¸. ÐÐ´Ð½Ð°ÐºÐ¾, ÑÑÐµÐ¿ÐµÐ½Ñ Ð¿ÐµÑÐµÐºÑÑÑÐ¸Ñ ÑÐ´ÐµÑ Ð½ÐµÐ»ÑÐ·Ñ Ð¸Ð·Ð¼ÐµÑÐ¸ÑÑ Ð² ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐµ. Ð Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¾Ñ ÑÐµÐ½ÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÐ¸ ÑÑÐ¾Ð»ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ñ ÑÐ¸Ð·Ð¸ÐºÐ° Ð¿ÑÐ¾ÑÐµÑÑÐ¾Ð² Ð·Ð½Ð°ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾ ÑÐ°Ð·Ð»Ð¸ÑÐ°ÐµÑÑÑ.Ð§Ð¸ÑÐ»Ð¾ ÑÐ°Ð½ÐµÐ½ÑÑ Ð½ÑÐºÐ»Ð¾Ð½Ð¾Ð² Â Ð¸ ÑÐ¸ÑÐ»Ð¾ Ð±Ð¸Ð½Ð°ÑÐ½ÑÑ Ð½ÑÐºÐ»Ð¾Ð½-Ð½ÑÐºÐ»Ð¾Ð½Ð½ÑÑ ÑÑÐ¾Ð»ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ð¹ Ð² ÑÐ¾Ð±ÑÑÐ¸Ð¸ Â â Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÑ, ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸Ð·ÑÑÑÐ¸Ðµ ÑÐµÐ½ÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑ, Ð½ÐµÐ²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ Ð¸Ð·Ð¼ÐµÑÐ¸ÑÑ Ð² ÑÐµÐ°Ð»ÑÐ½Ð¾Ð¼ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐµ [1]. Ð¦ÐµÐ»ÑÑ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð±Ñ Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ð»Ð° Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð½Ð°Ð±Ð»ÑÐ´Ð°ÐµÐ¼ÑÑ Ð² ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐµ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½, ÑÐ°ÐºÐ¸Ñ ÐºÐ°Ðº ÑÐ¸ÑÐ»Ð¾ Ð·Ð°ÑÑÐ¶ÐµÐ½Ð½ÑÑ ÑÐ°ÑÑÐ¸Ñ Ð¸ ÑÐ¸ÑÐ»Ð¾ Ð½ÐµÐ¹ÑÑÐ¾Ð½Ð¾Ð², ÑÐ¾Ð¶Ð´Ð°ÑÑÐ¸ÑÑÑ Ð²Ð¾ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ð¸, Ð¿ÑÐµÐ´ÑÐºÐ°Ð·ÑÐ²Ð°ÑÑ Ð½ÐµÐ½Ð°Ð±Ð»ÑÐ´Ð°ÐµÐ¼ÑÐµ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½Ñ, ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸Ð·ÑÑÑÐ¸Ðµ ÑÐµÐ½ÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑ, Ð° Ð¸Ð¼ÐµÐ½Ð½Ð¾ ÑÐ¸ÑÐ»Ð¾ ÑÐ°Ð½ÐµÐ½ÑÑ Ð½ÑÐºÐ»Ð¾Ð½Ð¾Ð², ÑÑÐ°ÑÑÐ²ÑÑÑÐ¸Ñ Ð²Ð¾ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ð¸, Ð¸ ÑÐ¸ÑÐ»Ð¾ Ð±Ð¸Ð½Ð°ÑÐ½ÑÑ Ð½ÑÐºÐ»Ð¾Ð½-Ð½ÑÐºÐ»Ð¾Ð½Ð½ÑÑ ÑÑÐ¾Ð»ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ð¹.Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸ÑÑÑ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¿ÑÐµÐ´ÑÐºÐ°Ð·Ð°Ð½Ð¸Ð¹ Â Ð¸ Â Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð½Ð°Ð±Ð»ÑÐ´Ð°ÐµÐ¼ÑÑ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½ Ð´Ð»Ñ ÑÑÐµÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ð¿ÑÐµÐ´Ð»Ð°Ð³Ð°ÐµÑÑÑ Ð²ÑÐ±ÑÐ°ÑÑ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½ÑÑ Ð¼Ð¾Ð´ÐµÐ»Ñ, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð±Ñ Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ð»Ð° Ñ Ð±Ð¾Ð»ÑÑÐµÐ¹ ÑÐ¾ÑÐ½Ð¾ÑÑÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÑÑ ÑÐµÐ½ÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑ ÑÐ´ÐµÑÐ½ÑÑ ÑÑÐ¾Ð»ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ð¹ Ð² ÑÐµÐ°Ð»ÑÐ½ÑÑ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ñ. Ð¢Ð°Ðº ÐºÐ°Ðº ÑÐµÐ»ÑÑ ÑÐ°Ð±Ð¾ÑÑ ÑÑÐ°Ð²Ð¸ÑÑÑ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð´Ð»Ñ Ð¿ÑÐµÐ´ÑÐºÐ°Ð·Ð°Ð½Ð¸Ñ Ð½ÐµÐ½Ð°Ð±Ð»ÑÐ´Ð°ÐµÐ¼ÑÑ Ð² ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐµ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½, ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐµ Ð´Ð°Ð½Ð½ÑÐµ Ð´Ð»Ñ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð½Ðµ Ð¿Ð¾Ð´ÑÐ¾Ð´ÑÑ. Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¾Ð±ÑÑÐ°Ð»Ð¸ÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð´Ð°Ð½Ð½ÑÑ, Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ Ð¸Ð· ÐÐ¾Ð½ÑÐµ-ÐÐ°ÑÐ»Ð¾ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¾ÑÐ° Ð²ÑÑÐ¾ÐºÐ¾ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐ´ÐµÑÐ½ÑÑ ÑÑÐ¾Ð»ÐºÐ½Ð¾Ð²ÐµÐ½Ð¸Ð¹ Pythia8/Angantyr [2].
description: One of the characteristics of collisions of nuclei is the centrality of the event, reflecting the degree of overlap between two colliding nuclei. The multiplicity of charged particles and the number of neutrons produced in the interaction are sensitive to the magnitude of centrality. Â However, the degree of overlap of the nuclei cannot be measured experimentally. Depending on the centrality of the collision, the physics of the processes varies significantly.The number of wounded nucleons Â and the number of binary nucleon-nucleon collisions in the event Â are parameters characterizing centrality that cannot be measured in a real experiment [1]. The main goal of the work is to develop an optimal machine learning model that would allow, based on the quantities observed in the experiment, such as the number of charged particles and the number of neutrons generated in the interaction, to predict unobservable quantities characterizing centrality, namely the number of wounded nucleons involved in the interaction and the number of binary nucleon-nucleon collisions.In this study, a comparative analysis of the predictions of Â and Â based on the observed values for three machine learning models is carried out. Based on the analysis, it is proposed to choose an optimal model that would allow determining the centrality of nuclear collisions in real experiments with greater accuracy. Since the aim of the work is to develop a model for predicting unobservable quantities in the experiment, experimental data are not suitable for training models. In this study, the models were trained using data obtained from the Monte Carlo generator of high-energy nuclear collisions Pythia8/Angantyr [2].