  In drug discovery, molecular dynamics (MD) simulation for protein-ligand
binding provides a powerful tool for predicting binding affinities, estimating
transport properties, and exploring pocket sites. There has been a long history
of improving the efficiency of MD simulations through better numerical methods
and, more recently, by utilizing machine learning (ML) methods. Yet, challenges
remain, such as accurate modeling of extended-timescale simulations. To address
this issue, we propose NeuralMD, the first ML surrogate that can facilitate
numerical MD and provide accurate simulations in protein-ligand binding. We
propose a principled approach that incorporates a novel physics-informed
multi-grained group symmetric framework. Specifically, we propose (1) a
BindingNet model that satisfies group symmetry using vector frames and captures
the multi-level protein-ligand interactions, and (2) an augmented neural
differential equation solver that learns the trajectory under Newtonian
mechanics. For the experiment, we design ten single-trajectory and three
multi-trajectory binding simulation tasks. We show the efficiency and
effectiveness of NeuralMD, with a 2000$\times$ speedup over standard numerical
MD simulation and outperforming all other ML approaches by up to 80% under the
stability metric. We further qualitatively show that NeuralMD reaches more
stable binding predictions compared to other machine learning methods.
