机器学习仿真中能重离子碰撞的集体流与核阻止本领

he nuclear equation of state (EoS) delineates the thermodynamic relationship between nucleon energy and nuclear matter density, temperature, and isospin asymmetry. This relationship is crucial for validating existing nuclear theoretical models, investigating the nature of nuclear forces, and understanding the structure of compact stars, neutron star mergers, and related astrophysical processes. Heavy-ion collisionexperiments combined with transport models is a critical way to explore the high-density behavior of EoS. With the rapid advancement of a new generation of high-current heavy-ion accelerators and the development of efficient detection technologies, the variety, volume, and precision of data generated from heavy-ion collision experiments have seen substantial enhancements. The effective utilization and analysis of these experimental datasets to extract crucial information about the EoS have emerged as one of the central challenges in contemporary heavy-ion physics research. Bayesian analysis is a statistical method, which can extract reliable physical information by comparing experimental data with theoretical calculations, and can quantify the uncertainty of parameters, so it has been widely concerned. In the task of determining the range of parameters of EoSby Bayesian inference.The Monte Carlo sampling method is used to extract observables from the final state particle information simulated by transport model ineach set of EoSparameters.Since the calculation process of transport model is complex, this step will consume a lot of time. This complexity significantly hinders the efficiency of data generation and limits the ability to explore the full parameter space. To address this challenge, there is a pressing need for a more efficient approach to simulate transport models, particularly one that leverages modern computational techniques to accelerate the process. Here, we propose a machine learning-based approach to develop a transport model emulator that can significantly reduce calculated time. We evaluate three machine learning algorithmsGaussian processes, Multi-task neural networks and random foreststo train emulatorsbased on the ultra-relativistic quantum molecular dynamics (UrQMD) transport model. The selected observables are protons directed flow, elliptical flow and nuclear stopping extracted from the final state of the Au+Au collision at Elab= 0.25 GeV/nucleonindifferent EoS parameters (incompressibility K0, effective massm*and in-medium correction factorF of nucleon-nucleon elastic cross section). 150 parameter sets of the UrQMD model with K0 = 180, 220, 260, 300, 340, 380 MeV, m*/m = 0.6, 0.7, 0.8, 0.9, 0.95 and F = 0.6, 0.7, 0.8, 0.9, 1.0 are run. For each case, 2105 events with the reduced impact parameter b0<0.45 are simulated in order to make sure that the statistical errors are negligible. The results from the calculations with the above mention 150 parameter sets are fed to three machine learning algorithm to train the emulators. In addition, 20 parameter sets of the UrQMD model with randomly chosen K0, m*, and F are run and the results on observables are used to test the performance of the emulators. The results obtained from Gauss processes and multi-task neural networks are in line with the one calculated by UrQMD model, indicating that the two emulators has a high accuracy and can be used during the Bayesian analysis. However, when predicting and with reduced impact parameter b0 < 0.25, some data points predicted by random forest have large errors, indicating that the random forest as a transport model emulator is relatively poor in predicting the observables. In order to further compare the prediction effect of the three transport model emulators, we choose the coefficient of determination R2 as the evaluation index. The R of Gaussian process, multi-task neural network and random forest in the test set are 0.95, 0.93, and 0.85, respectively.These results show that both Gaussian process and multi-task neural network show high accuracy when simulating the data of UrQMD model, and can effectively accelerate the calculation process. However, for complex tasks with a large number of parameters and observables, the efficiency and accuracy of Gaussian processes emulator may suffer. Thus, relying solely on Gaussian processes may not suffice. In this case, multi-task neural networks show greater adaptability, is better able to handle complex data sets and effectively learn information within parameter spaces. To sum up, Gaussian processes generally perform well in Bayesian frameworks as the choice of a transport model emulator, especially for moderate data sets, while multi-task neural networks may be a more ideal choice for complex tasks with more parameters and observables. In practical application, the more suitable emulator should be selected according to the specific task requirements and data characteristics.