MLMD: Machine Learning Velocities to Propagate Molecular Dynamics Simulations

Temporal evolution in molecular dynamics (MD) simulations requires updates on particle velocities. These updates are obtained from forces that are computed traditionally from physics-based Hamiltonians, and more recently from machine-learned (ML) numerical forms. An alternative strategy that is being explored is to predict velocity updates from ML models without concerning with energy or force calculations. The key advantages of this strategy are that bypassing force calculations, especially when dealing with quantum mechanical Hamiltonians, should effectively speed up MD simulations, and such ML predictors can also be trained on the fly. Here we take this development to the next stage by showing how ML velocity predictors can be incorporated into MD integrators to propagate trajectories accurately. In addition, we explore a new type of ML velocity predictor that is trained exclusively on historical particle velocities, where we exploit the fact that particle velocities are inherently auto-correlated in time. We show how stacked long short-term memory neural networks can be trained to accomplish these tasks and propagate trajectories that conserve energy, structure and dynamics. The fascinating aspect is that structure and energies are conserved without actually predicting them directly. Trajectories do tend to accumulate errors upon continual use of ML velocity predictions, despite velocity prediction accuracy being greater than 99.9%. Nevertheless, we show that error accumulation can be controlled and MD stability can be rescued by making periodic injections of velocity updates computed from Hamiltonians (frequency ≤ 0.01). We propose this proof-of-concept machine-learned MD (MLMD) protocol using a series of harmonic oscillators, laying the foundation necessary to extending its applications to complex systems.