用机器学习快速识别聚合物链的拓扑结构，准确率达97%。
Writhe-Based Polymer Link Classification Using Machine Learning
- 基于扭结密度矩阵训练前馈神经网络
- 对六种初等链接分类准确率97%，跨温度长度稳定
- 适合研究复杂拓扑如博罗梅恩环的快速分析
绳结与链环的快速准确分类是数学与(生物)物理系统中的开放难题，涉及聚合物熔体、DNA和蛋白质。本文提出数据驱动方法，扩展了先前框架（Sleiman et al, 2024 Soft Matter, 20(1), pp.71-78），利用训练于扭结密度矩阵的前馈神经网络，在热平衡配置下对前六种初等链接实现97%分类准确率。该准确率在不同温度与链长下保持稳定，但随拓扑扰动的高斯噪声增加而迅速下降，表明扭结密度矩阵对拓扑敏感。结果证明基于扭结密度矩阵的神经网络可高效分类双组分链接，为复杂链拓扑（如博罗梅恩环或多组分链接）提供可行工具，克服精确计算拓扑不变量的高昂计算成本。
原文摘要 · Abstract (English)
Unique and rapid classification of knots and links is an open mathematical problem that is relevant to a range of (bio)physical systems, including polymer melts, DNA, and proteins. In this paper, we explore a data-driven approach to the classification problem of link topology. Extending the framework introduced in Ref. 1 (Sleiman et al, 2024 Soft Matter, 20(1), pp.71-78), we show that a feedforward neural network trained on the writhe density matrix classifies thermally equilibrated configurations of the first six prime links with 97% accuracy. We demonstrate that this accuracy remains high across a range of temperatures and lengths of link components, while rapidly deteriorating with the addition of topology-altering Gaussian noise; a result consistent with the writhe density matrix containing features sensitive to topology. Our results show that neural networks based on the writhe density matrix efficiently classify two-component links, establishing machine learning as a promising tool for rapid classification of more complex link topologies, e.g. Borromean rings and multi-component links, as the computational cost of exact numerical calculation of topological invariants becomes prohibitive.
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