Identifying knot types of polymer conformations by machine learning

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.