Velocity Updates from Machine Learning for Stable Molecular Dynamics Integration

We present a machine-augmented molecular dynamics (MAMD) framework in which particle velocities are updated using predictions from stacked long short-term memory (LSTM) networks trained on historical velocity and coordinate data. MAMD propagates coordinate trajectories in time without access to forces or energies during training or inference. Applied to isolated harmonic diatomics, MAMD conserves total energy, preserves molecular structure, and reproduces velocity autocorrelation functions. Small integration errors can accumulate over long trajectories, but we show that molecular dynamics stability can be recovered through periodic, but infrequent injections of velocity updates computed from Hamiltonian forces (frequency ≤ 0.01). We also find that the optimal history length for each diatom closely matches the first inflection point of its velocity autocorrelation function, suggesting a link between model architecture and statistical mechanics. These results demonstrate the feasibility of MAMD as a proof-of-concept integration strategy, in which finite velocity memory supports short-horizon predictions and sparse Hamiltonian check-ins provide long-horizon stability. Specifically, we show that force-free, velocity-based machine learning updates can be embedded directly into conventional molecular dynamics algorithms while retaining essential physical invariants, providing a physically interpretable basis for hybrid MD/ML integration.