AI 中文总结
本文提出基于条件流匹配（CFM）的代理模型，通过扩展交叉注意力的Cross-Attention-CFM及结合少量传统跟踪粒子的Hybrid-CFM，实现粒子跟踪的高效高精度模拟，速度较传统方法提升三个数量级，降低代理模型构建成本。
AI 中文摘要
粒子跟踪是粒子加速器设计与优化的基础工具。传统跟踪例程精度高，但计算量大，尤其在模拟大量粒子集合或长时间跨度时，优化中高维参数空间极具挑战性，实时代理模型在诸多应用中仍难以实现。本文提出一种基于条件流匹配（CFM）的代理建模方法：在欧洲核子中心（CERN）质子同步加速器（PS）的跟踪模拟数据上，针对10维参数空间训练CFM模型，该模型复现最终相空间分布的中位数平方最大均值差异（MMD²）为3×10⁻⁴，平均推理时间0.04秒，比传统跟踪快三个数量级；为捕获普通CFM无法表示的依赖分布的动力学，本文通过对初始粒子集合添加交叉注意力（Cross-Attention-CFM）扩展模型，实验表明该扩展可恢复PS中空间电荷基准的性能，而普通CFM在此基准上性能下降；最后，本文提出Hybrid-CFM，该模型利用少量传统跟踪粒子为模型提供信息，在相同10维PS任务中，采用100个辅助粒子、在200个分布上训练的Hybrid-CFM，性能与在1500个分布上训练的普通CFM相当，且最坏情况（第90百分位）MMD²提升约4倍，大幅降低构建代理模型的前期成本。
英文摘要
Particle tracking is a fundamental tool for particle-accelerator design and optimisation. Conventional tracking routines provide high accuracy but are computationally demanding, especially when simulating large particle ensembles or long time spans. As a result, optimising moderate- to high-dimensional parameter spaces is challenging, and real-time surrogate models remain out of reach for many applications. This contribution introduces a surrogate-modelling approach based on conditional flow matching (CFM). A CFM model is trained on tracking simulations of CERN's Proton Synchrotron (PS) over a 10-dimensional parameter space. The trained model reproduces final phase-space distributions with a median squared maximum mean discrepancy MMD$^2$ of $3\times 10^{-4}$ and mean inference time of 0.04 s, a speed-up of three orders of magnitude over conventional tracking. To capture distribution-dependent dynamics that vanilla CFM cannot represent, we extend the model with cross-attention over the initial particle ensemble (Cross-Attention-CFM) and demonstrate that this extension recovers performance on a space-charge benchmark in the PS, where vanilla CFM degrades. Finally, we introduce Hybrid-CFM, in which a small number of conventionally-tracked particles are used to inform the model. On the same 10-dimensional PS task, Hybrid-CFM with 100 auxiliary particles trained on 200 distributions matches the vanilla CFM trained on 1500, and improves the worst-case (90th-percentile) MMD$^2$ by roughly a factor of four, substantially reducing the upfront cost of building a surrogate.
Comments19 pages, 8 figures
