发表机构
Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对双部分子分布的高维网格存储问题，提出混合神经网络方法，以稀疏表补充网络预测，显著降低存储和内存开销，仅轻微牺牲评估速度。
AI 中文摘要
传统的基于网格的方法用于存储和评估普通部分子分布函数（PDFs），例如在LHAPDF中实现的方法，对于双部分子分布（DPDs）来说变得更为苛刻。虽然共线PDF依赖于一个纵向动量分数和一个因子化尺度，但不等尺度DPD对于每个部分子味组合依赖于两个动量分数和两个独立的因子化尺度。因此，直接表格化这种四维依赖性需要显著更多的磁盘空间和运行时内存。在本工作中，我们开发了一种混合神经网络方法，用于紧凑存储和快速评估$y$-独立的不等尺度DPDs。该网络通过重现参考网格的大部分值来压缩网格，而原始值仅存储在神经预测未达到所需精度的点上。通过这种方式，神经模型捕获了网格的主体，而稀疏表覆盖了剩余的困难点。对于此处研究的基于GS09的密集网格，仅需将$0.694\%$的活动味值存储在稀疏表中。与压缩的密集网格相比，混合方法将磁盘占用减少了$10.6$倍，峰值内存使用减少了$31.6$倍，初始化时间减少了约$10.6$倍。同时，其评估吞吐量达到密集网格速率的约$85\%$。该方法在PDFxTMDLib中以C++原生实现，运行时不需要Python或PyTorch。因此，混合方案提供了更低的存储和启动成本，仅以评估速度的适度降低为代价。
英文摘要
The conventional grid-based approach used for storing and evaluating ordinary parton distribution functions (PDFs), as implemented for example in LHAPDF, becomes much more demanding for double parton distributions (DPDs). While a collinear PDF depends on one longitudinal momentum fraction and one factorization scale, an unequal-scale DPD depends on two momentum fractions and two independent factorization scales for every parton-flavor combination. Direct tabulation of this four-dimensional dependence therefore requires considerably more disk space and runtime memory. In this work, we develop a hybrid neural-network method for compact storage and fast evaluation of $y$-independent unequal-scale DPDs. The network compresses the reference grid by reproducing most of its values, while the original values are stored only at points where the neural prediction does not reach the required accuracy. In this way, the neural model captures the bulk of the grid, with a sparse table covering the remaining difficult points. For the GS09-based dense grid studied here, only $0.694\%$ of the active flavor values need to be stored in the sparse table. Compared with the compressed dense grid, the hybrid method reduces the disk footprint by a factor of $10.6$, peak memory use by a factor of $31.6$, and initialization time by about a factor of $10.6$. At the same time, its evaluation throughput reaches about $85\%$ of the dense-grid rate. The method is implemented natively in C++ within PDFxTMDLib and requires neither Python nor PyTorch at runtime. The hybrid scheme therefore offers much lower memory and startup costs, with only a modest reduction in evaluation speed.
