用AI模型在线逐步还原费曼积分,突破传统方法的内存瓶颈。
Learning to Unscramble Feynman Loop Integrals with SAILIR
- 用自监督Transformer模型学习逆转积分混淆步骤
- 复杂度升高时内存几乎不变,最复杂情况仅需Kira 40%内存
- 适合高复杂度积分计算,可解决传统方法无法处理的问题
费曼积分的积分-分部(IBP)约化是高能物理精确计算的关键瓶颈。传统基于拉普托拉算法的方法需解大规模方程组,内存消耗随积分复杂度快速上升。我们提出SAILIR(基于自监督AI的环积分约化),一种基于Transformer分类器的机器学习方法,可在线逐步引导积分约化。该分类器通过反向应用已知约化恒等式生成复杂表达式,在合成数据上进行自监督训练。结合束搜索与高度并行、异步、单轮次约化策略,SAILIR可对任意高权重积分进行约化且内存恒定。在两圈三角-盒拓扑上,与当前最优代码Kira对比16个不同复杂度积分:虽墙钟时间较慢,但每工作节点内存几乎不随复杂度增长;对于最复杂积分,仅需Kira 40%内存,同时达到相近约化速度。这证明了一种全新的IBP约化范式,有望彻底克服拉普托拉方法的内存瓶颈,使当前不可行的高精度计算成为可能。
原文摘要 · Abstract (English)
Integration-by-parts (IBP) reduction of Feynman integrals to master integrals is a key computational bottleneck in precision calculations in high-energy physics. Traditional approaches based on the Laporta algorithm require solving large systems of equations, leading to memory consumption that grows rapidly with integral complexity. We present SAILIR (Self-supervised AI for Loop Integral Reduction), a new machine learning approach in which a transformer-based classifier guides the reduction of integrals one step at a time in a fully online fashion. The classifier is trained in an entirely self-supervised manner on synthetic data generated by a scramble/unscramble procedure: known reduction identities are applied in reverse to build expressions of increasing complexity, and the classifier learns to undo these steps. When combined with beam search and a highly parallelized, asynchronous, single-episode reduction strategy, SAILIR can reduce integrals of arbitrarily high weight with bounded memory. We benchmark SAILIR on the two-loop triangle-box topology, comparing against the state-of-the-art IBP reduction code Kira across 16 integrals of varying complexity. While SAILIR is slower in wall-clock time, its per-worker memory consumption remains approximately flat regardless of integral complexity, in contrast to Kira whose memory grows rapidly with complexity. For the most complex integrals considered here, SAILIR uses only 40\% of the memory of Kira while achieving comparable reduction times. This demonstrates a fundamentally new paradigm for IBP reduction in which the memory bottleneck of Laporta-based approaches could be entirely overcome, potentially opening the door to precision calculations that are currently intractable.
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