Identifying knot types of polymer conformations by machine learning

Olafs Vandans City University of Hong Kong Kaiyuan Yang National University of Singapore Zhongtao Wu Chinese University of Hong Kong Liang Dai City University of Hong Kong

Machine Learning mathscidoc:2307.41001

Physical Review E, 101, 2020.2
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.
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  • "Nature" Research Highlight (; Feature in "Physics" (
  title={Identifying knot types of polymer conformations by machine learning},
  author={Olafs Vandans, Kaiyuan Yang, Zhongtao Wu, and Liang Dai},
  booktitle={Physical Review E},
Olafs Vandans, Kaiyuan Yang, Zhongtao Wu, and Liang Dai. Identifying knot types of polymer conformations by machine learning. 2020. Vol. 101. In Physical Review E.
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