PhysGNO: Physics-Guided Graph Neural Operators for Molecular Dynamics

Molecular dynamics (MD) plays a central role in scientific applications such as drug discovery, materials design, and chemical reaction analysis. Recent advances in deep learning have further expanded the capabilities of MD modeling. In particular, graph neural network-based interatomic potentials have achieved remarkable success in modeling molecular interactions, enabling accurate prediction of molecular energies and forces while effectively preserving physical information. However, these methods still rely on a large number of iterative integration steps to simulate long-horizon trajectories. Neural operators provide a complementary paradigm by learning trajectory evolution without step-by-step integration, thereby offering significantly improved efficiency. Nevertheless, such data-driven approaches often lack sufficient physical priors, which limits their ability to produce accurate molecular trajectories. To address these challenges, we propose PhysGNO, a physics-guided neural operator for molecular trajectory learning. PhysGNO leverages physical information captured by potential energy networks to guide trajectory evolution, combining the efficiency of neural operators with physically meaningful inductive bias for accurate trajectory prediction. In addition, PhysGNO incorporates molecular flexibility and rich vector-valued features into its spatiotemporal evolution layers, making it better suited to molecular dynamics systems. Extensive experiments on MD17, rMD17, and MD22 demonstrate the effectiveness and efficiency of the proposed method.