Variational autoencoders understand knot topology
This work addresses the challenge of knot classification in polymers, offering a novel ML-based alternative to standard mathematical methods, though it is incremental as it builds on existing VAEs.
The researchers tackled the problem of identifying knots in polymers by introducing a hybrid supervised/unsupervised machine learning approach using a variational autoencoder with a classifier (VAEC), which successfully distinguished complex topological features like chirality and generated knotted configurations without simulations, achieving accurate chirality detection for knots not in the training set.
Supervised machine learning (ML) methods are emerging as valid alternatives to standard mathematical methods for identifying knots in long, collapsed polymers. Here, we introduce a hybrid supervised/unsupervised ML approach for knot classification based on a variational autoencoder enhanced with a knot type classifier (VAEC). The neat organization of knots in its latent representation suggests that the VAEC, only based on an arbitrary labeling of three-dimensional configurations, has grasped complex topological concepts such as chirality, unknotting number, braid index, and the grouping in families such as achiral, torus, and twist knots. The understanding of topological concepts is confirmed by the ability of the VAEC to distinguish the chirality of knots $9_{42}$ and $10_{71}$ not used for its training and with a notoriously undetected chirality to standard tools. The well-organized latent space is also key for generating configurations with the decoder that reliably preserves the topology of the input ones. Our findings demonstrate the ability of a hybrid supervised-generative ML algorithm to capture different topological features of entangled filaments and to exploit this knowledge to faithfully reconstruct or produce new knotted configurations without simulations.