Machine learning understands knotted polymers

Abstract: Simulated configurations of flexible knotted rings confined inside a spherical cavity are fed into long-short term memory neural networks (LSTM NNs) designed to distinguish knot types. The results show that they perform well in knot recognition even if tested against flexible, strongly confined and therefore highly geometrically entangled rings. In agreement with the expectation that knots are delocalized in dense polymers, a suitable coarse-graining procedure on configurations boosts the performance of the LSTMs when knot identification is applied to rings much longer than those used for training. Notably, when the NNs fail, usually the wrong prediction still belongs to the same topological family of the correct one. The fact that the LSTMs are able to grasp some basic properties of the ring's topology is corroborated by a test on knot types not used for training. We also show that the choice of the NN architecture is important: simpler convolutional NNs do not perform so well. Finally, all results depend on the features used for input: surprisingly, coordinates or bond directions of the configurations provide the best accuracy to the NNs, even if they are not invariant under rotations (while the knot type is invariant). Other rotational invariant features we tested are based on distances, angles, and dihedral angles.