{"title":"利用自动微分改进巴利茨基-科夫切戈夫演化方程的求解器","authors":"Florian Cougoulic, Piotr Korcyl, Tomasz Stebel","doi":"10.1016/j.cpc.2025.109616","DOIUrl":null,"url":null,"abstract":"<div><div>The Balitsky-Kovchegov (BK) evolution equation is an equation derived from perturbative Quantum Chromodynamics that allows one to evolve with collision energy the scattering amplitude of a pair of quark and antiquark off a hadron target, called the dipole amplitude. The initial condition, being a non-perturbative object, usually has to be modeled separately. Typically, the model contains several tunable parameters that are determined by fitting to experimental data. In this contribution, we propose an implementation of the BK solver using differentiable programming. Automatic differentiation offers the possibility that the first and second derivatives of the amplitude with respect to the initial condition parameters are automatically calculated at all stages of the simulation. This fact should considerably facilitate and speed up the fitting step. Moreover, in the context of Transverse Momentum Distributions (TMD), we demonstrate that automatic differentiation can be used to obtain the first and second derivatives of the amplitude with respect to the quark-antiquark separation. These derivatives can be used to relate various TMD functions to the dipole amplitude. Our C++ code for the solver, which is available in a public repository <span><span>[1]</span></span>, includes the Balitsky one-loop running coupling prescription and the kinematic constraint. This version of the BK equation is widely used in the small-<em>x</em> evolution framework.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"313 ","pages":"Article 109616"},"PeriodicalIF":7.2000,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Improving the solver for the Balitsky-Kovchegov evolution equation with Automatic Differentiation\",\"authors\":\"Florian Cougoulic, Piotr Korcyl, Tomasz Stebel\",\"doi\":\"10.1016/j.cpc.2025.109616\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The Balitsky-Kovchegov (BK) evolution equation is an equation derived from perturbative Quantum Chromodynamics that allows one to evolve with collision energy the scattering amplitude of a pair of quark and antiquark off a hadron target, called the dipole amplitude. The initial condition, being a non-perturbative object, usually has to be modeled separately. Typically, the model contains several tunable parameters that are determined by fitting to experimental data. In this contribution, we propose an implementation of the BK solver using differentiable programming. Automatic differentiation offers the possibility that the first and second derivatives of the amplitude with respect to the initial condition parameters are automatically calculated at all stages of the simulation. This fact should considerably facilitate and speed up the fitting step. Moreover, in the context of Transverse Momentum Distributions (TMD), we demonstrate that automatic differentiation can be used to obtain the first and second derivatives of the amplitude with respect to the quark-antiquark separation. These derivatives can be used to relate various TMD functions to the dipole amplitude. Our C++ code for the solver, which is available in a public repository <span><span>[1]</span></span>, includes the Balitsky one-loop running coupling prescription and the kinematic constraint. This version of the BK equation is widely used in the small-<em>x</em> evolution framework.</div></div>\",\"PeriodicalId\":285,\"journal\":{\"name\":\"Computer Physics Communications\",\"volume\":\"313 \",\"pages\":\"Article 109616\"},\"PeriodicalIF\":7.2000,\"publicationDate\":\"2025-04-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Physics Communications\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0010465525001183\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Physics Communications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0010465525001183","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
摘要
巴利茨基-科夫切戈夫(Balitsky-Kovchegov,BK)演化方程是从微扰量子色动力学中推导出来的一个方程,它可以使一对夸克和反夸克离开强子目标时的散射振幅(称为偶极振幅)随碰撞能量而演化。初始条件是一个非微扰对象,通常需要单独建模。通常情况下,模型包含几个通过拟合实验数据确定的可调参数。在本文中,我们提出了使用可微分编程实现 BK 求解器的方法。自动微分可以在模拟的各个阶段自动计算振幅相对于初始条件参数的一阶和二阶导数。这将大大方便和加快拟合步骤。此外,在横向动量分布(TMD)的背景下,我们证明了自动微分可用于获得振幅相对于夸克-反夸克分离的一阶和二阶导数。这些导数可用于将各种 TMD 函数与偶极子振幅联系起来。我们用于求解器的 C++ 代码可在公共存储库[1]中获得,其中包括巴利茨基单环运行耦合处方和运动学约束。这一版本的 BK 方程广泛应用于小 x 演化框架。
Improving the solver for the Balitsky-Kovchegov evolution equation with Automatic Differentiation
The Balitsky-Kovchegov (BK) evolution equation is an equation derived from perturbative Quantum Chromodynamics that allows one to evolve with collision energy the scattering amplitude of a pair of quark and antiquark off a hadron target, called the dipole amplitude. The initial condition, being a non-perturbative object, usually has to be modeled separately. Typically, the model contains several tunable parameters that are determined by fitting to experimental data. In this contribution, we propose an implementation of the BK solver using differentiable programming. Automatic differentiation offers the possibility that the first and second derivatives of the amplitude with respect to the initial condition parameters are automatically calculated at all stages of the simulation. This fact should considerably facilitate and speed up the fitting step. Moreover, in the context of Transverse Momentum Distributions (TMD), we demonstrate that automatic differentiation can be used to obtain the first and second derivatives of the amplitude with respect to the quark-antiquark separation. These derivatives can be used to relate various TMD functions to the dipole amplitude. Our C++ code for the solver, which is available in a public repository [1], includes the Balitsky one-loop running coupling prescription and the kinematic constraint. This version of the BK equation is widely used in the small-x evolution framework.
期刊介绍:
The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper.
Computer Programs in Physics (CPiP)
These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged.
Computational Physics Papers (CP)
These are research papers in, but are not limited to, the following themes across computational physics and related disciplines.
mathematical and numerical methods and algorithms;
computational models including those associated with the design, control and analysis of experiments; and
algebraic computation.
Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.