发表机构
School of Physics and Astronomy, The University of Edinburgh; School of Mathematics, The University of Edinburgh; MRC Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh（物理与天文学学院，爱丁堡大学; 数学学院，爱丁堡大学; 人类遗传学单位，遗传与癌症研究所，爱丁堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究链环拓扑分类问题，核心方法是基于缠绕数密度矩阵训练前馈神经网络，主要贡献是能高效分类双组件链环，准确率高且在一定条件下稳定，为复杂链环拓扑快速分类提供了有前景的工具。
AI 中文摘要
结和链环的独特快速分类是一个开放的数学问题，与包括聚合物熔体、DNA和蛋白质在内的一系列（生物）物理系统相关。本文探索了一种数据驱动的链环拓扑分类方法。扩展文献1中的框架，我们表明在前六个素数链环的热平衡构型上训练的前馈神经网络，分类准确率达97%。该准确率在一定温度和链环组件长度范围内保持较高，添加拓扑改变的高斯噪声时迅速下降。结果表明基于缠绕数密度矩阵的神经网络能有效分类双组件链环，为更复杂链环拓扑的快速分类建立了机器学习这一有前景的工具。
英文摘要
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.
Comments8 pages, 4 figures
