摘要
重离子碰撞实验结合输运模型模拟是提取核物质性质信息的重要手段之一。贝叶斯分析是一种能够从实验数据与理论计算的比较中提取信息的统计方法,因此得到广泛应用。在此过程中,通常需借助马尔可夫链蒙特卡罗方法在参数空间中进行采样,并随后开展输运模型模拟计算。然而,由于输运模型的计算复杂且耗时较长,为提高效率,可通过机器学习算法训练一个输运模型仿真器。本文采用高斯过程、多任务神经网络和随机森林三种机器学习算法,对极端相对论量子分子动力学(Ultra-relativistic Quantum Molecular Dynamics,UrQMD)输运模型仿真器进行训练。在与核物质性质相关的三个参数的先验分布范围内,选取了150组参数的结果作为训练集,并通过UrQMD输运模型模拟这些参数下入射能量为每核子0.25 GeV的金金碰撞。从末态粒子信息中提取自由质子的直接流、椭圆流以及核阻止本领等观测量。此外,随机选取20组参数的结果作为测试集以验证仿真器的效果。结果显示:高斯过程、多任务神经网络和随机森林三种算法在测试集上的预测结果决定系数R^(2)分别为0.95、0.93和0.85,这表明高斯过程和多任务神经网络在模拟输运模型计算的观测量时具有较高的准确性,能够显著加速输运模型的计算过程。
[Background]The nuclear equation of state(EoS)delineates the thermodynamic relationship between nucleon energy and nuclear matter density,temperature,and isospin asymmetry.This relationship is essential 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 phenomena.Heavy-ion collision experiments combined with transport models serve as a pivotal method to explore the high-density behavior of the EoS.With the rapid development of next-generation high-current heavy-ion accelerators and advanced detection technologies,the variety,volume,and precision of data generated from heavy-ion collision experiments have significantly improved.Effectively utilizing and analyzing these experimental datasets to extract critical insights into the EoS represents one of the central challenges in contemporary heavy-ion physics research.Bayesian analysis,a statistical approach,can extract reliable physical information by comparing experimental data with theoretical calculations and quantifying parameter uncertainties,thereby gaining widespread attention.In determining the range of EoS parameters using Bayesian inference,Monte Carlo sampling is employed to extract observables from finalstate particle information simulated by transport models under various EoS parameters.However,the complexity of transport model calculations significantly hinders data generation efficiency and limits exploration of the full parameter space.[Purpose]This study aims to a more efficient approach to simulate transport models,particularly one that leverages modern computational techniques to accelerate the process.[Methods]Here,a machine learningbased approach was proposed to develop a transport model emulator capable of significantly reducing computation time.We evaluate three machine learning algorithms—Gaussian processes,multi-task neural networks,and random forests—to train emulators based on the UrQMD transport model.The selected observables include protons'directed flow,elliptical flow,and nuclear stopping extracted from the final state of Au+Au collisions at Elab=0.25 GeV/nucleon under different EoS parameters(incompressibility K0,effective mass m*,and in-medium correction factor F for nucleon-nucleon elastic cross sections).A total of 150 parameter sets of the UrQMD model are run,with K_(0)=180 MeV,220 MeV,260 MeV,300 MeV,340 MeV,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.For each case,2×10^(5) events with a reduced impact parameter b0<0.45 are simulated to ensure negligible statistical errors.The results from these 150 parameter sets are used to train the emulators via the three machine learning algorithms.Additionally,20 parameter sets of the UrQMD model with randomly chosen K_(0),m*,and F are run,and the resulting observables are used to test emulator performance.[Results]The results obtained from Gaussian processes and multi-task neural networks align with those calculated by the UrQMD model,indicating high accuracy and suitability for use in Bayesian analysis.However,when predicting v11 and v20 with a reduced impact parameter b0<0.25,some data points predicted by random forests exhibit significant errors,suggesting that random forests are relatively less effective in predicting observables.To further compare the prediction performance of the three emulators,we use the coefficient of determination R^(2) as the evaluation index.The R^(2) values for Gaussian processes,multi-task neural networks,and random forests in the test set are 0.95,0.93,and 0.85,respectively.These results demonstrate that both Gaussian processes and multi-task neural networks achieve high accuracy when simulating UrQMD model data and can effectively accelerate the calculation process.However,for complex tasks involving a large number of parameters and observables,the efficiency and accuracy of Gaussian processes may decline.Thus,relying solely on Gaussian processes may be insufficient.In such cases,multi-task neural networks exhibit greater adaptability,better handling of complex datasets,and enhanced capability to learn information within parameter spaces.[Conclusions]In summary,Gaussian processes generally perform well within Bayesian frameworks as transport model emulators,particularly for moderate-sized datasets,while multi-task neural networks may be a more suitable choice for complex tasks involving numerous parameters and observables.In practical applications,the most appropriate emulator should be selected based on specific task requirements and data characteristics.
作者
魏国俊
王永佳
李庆峰
刘福虎
WEI Guojun;WANG Yongjia;LI Qingfeng;LIU Fuhu(Institute of Theoretical Physics,Shanxi University,Taiyuan 030006,China;School of Science,Huzhou University,Huzhou 313000,China)
出处
《核技术》
北大核心
2025年第5期42-52,共11页
Nuclear Techniques
基金
国家自然科学基金(No.12335008)
国家重点研发计划(No.2023YFA1606402)
等离子体物理全国重点实验室基金(No.6142A04230203)
浙江省教育厅科研项目(No.Y202353782)
湖州市自然科学基金(No.2024YZ28)资助。
关键词
重离子碰撞
核物质状态方程
输运模型
机器学习
仿真器
Heavy-ion collisions
Nuclear equation of state
Transport model
Machine learning
Emulator
