We investigate the use of artificial neural networks (NNs) as an alternative tool to current analytical methods
for recognizing knots in a given polymer conformation. The motivation is twofold. First, it is of interest to
examine whether NNs are effective at learning the global and sequential properties that uniquely define a knot.
Second, knot classification is an important and unsolved problem in mathematical and physical sciences, and
NNs may provide insights into this problem. Motivated by these points, we generate millions of polymer
conformations for five knot types: 0, 3_1, 4_1, 5_1, and 5_2, and we design various NN models for classification.
Our best model achieves a five-class classification accuracy of above 99% on a polymer of 100 monomers. We
find that the sequential modeling ability of recurrent NNs is crucial for this result, as it outperforms feed-forward
NNs and successfully generalizes to differently sized conformations as well. We present our methods and suggest
that deep learning may be used in specific applications of knot detection where some error is permissible.
Hopefully, with further development, NNs can offer an alternative computational method for knot identification
and facilitate knot research in mathematical and physical sciences.
Yijie WangComputer Science Department, Indiana University BloomingtonYuan ZhouYau Mathematical Sciences Center and Department of Mathematical Sciences, Tsinghua UniversityXiaoqing HuangDepartment of Biostatistics & Health Data Science, Indiana UniversityKun HuangDepartment of Biostatistics & Health Data Science, Indiana UniversityJie ZhangDepartment of Medical and Molecular Genetics, Indiana UniversityJianzhu MaInstitute for AI Industry Research, Tsinghua University
International Conference on Learning Representations (ICLR), 2023.5
Zihan ZhangDepartment of Automation, Tsinghua UniversityYuhang JiangDepartment of Automation, Tsinghua UniversityYuan ZhouYau Mathematical Sciences Center & Department of Mathematical Sciences, Tsinghua UniversityXiangyang JiDepartment of Automation, Tsinghua University
Conference on Neural Information Processing Systems (NeurIPS), 2022.12
Boxiao ChenCollege of Business Administration, University of Illinois at ChicagoDavid Simchi-LeviInstitute for Data, Systems and Society, Operations Research Center, Department of Civil and Environmental Engineering, Massachusetts Institute of TechnologyYining WangWarrington College of Business, University of FloridaYuan ZhouYanqi Lake Beijing Institute of Mathematical Science and Applications