Generative Modeling of Entangled Polymers with a Distance-Based Variational Autoencoder

We present a variational autoencoder framework for learning and generating configurations of structured polymer globules from distance matrices. We used coarse-grained molecular dynamics to sample polyethylene structures, which we used as the training set for our deep learning model. By combining convolution and attention layers, the model encodes the structural patterns of distance matrices into an organized and rototranslationally invariant latent space of lower dimensionality. The generative capability of the variational autoencoder, coupled with a postprocessing pipeline based on multidimensional scaling and short molecular dynamics, enables the recovery of physically meaningful configurations. The reconstructed and generated samples reproduce key observables, including energy, size, and entanglement, despite minor discrepancies in the raw decoder output. Interestingly, the length of the molecular dynamics relaxation required to generate canonical structures starting from the decoder outputs is 1 order of magnitude smaller than the corresponding relaxation time needed to sample structures using a pure MD approach, suggesting that our method can offer computational advantages in sampling uncorrelated structures.