Unsupervised learning of progress coordinates during weighted ensemble simulations: Application to millisecond protein folding

A major challenge for many rare-event sampling strategies is the identification of progress coordinates that capture the slowest relevant motions. Machine-learning methods that can identify progress coordinates in an unsupervised manner have therefore been of great interest to the simulation community. Here, we developed a general method for identifying progress coordinates "on-the-fly" during weighted ensemble (WE) rare-event sampling via deep learning (DL) of outliers among sampled conformations. Our method identifies outliers in a latent space model of the systems sampled conformations that is periodically trained using a convolutional variational autoencoder. As a proof of principle, we applied our DL-enhanced WE method to simulate a millisecond protein folding process. To enable rapid tests, our simulations propagated discrete-state synthetic molecular dynamics trajectories using a generative, fine-grained Markov state model. Results revealed that our on-the-fly DL of outliers enhanced the efficiency of WE by >3-fold in estimating the folding rate constant. Our efforts are a significant step forward in the unsupervised learning of slow coordinates during rare event sampling.