Geometric Graph Neural Diffusion for Stable Molecular Dynamics

Geometric graph neural networks (Geo-GNNs) have revolutionized molecular dynamics (MD) simulations by providing accurate and fast energy and force predictions. However, minor prediction errors could still destabilize MD trajectories in real MD simulations due to the limited coverage of molecular conformations in training datasets. Existing methods that focus on in-distribution predictions often fail to address extrapolation to unseen conformations, undermining the simulation stability. To tackle this, we propose Geometric Graph Neural Diffusion (GGND), a novel framework that can capture geometrically invariant topological features, thereby alleviating error accumulation and ensuring stable MD simulations. The core of our framework is that it iteratively refines atomic representations, enabling instantaneous information flow between arbitrary atomic pairs while maintaining equivariance. Our proposed GGND is a plug-and-play module that can seamlessly integrate with existing local equivariant message-passing frameworks, enhancing their predictive performance and simulation stability. We conducted sets of experiments on the 3BPA and SAMD23 benchmark datasets, which encompass diverse molecular conformations across varied temperatures. We also ran real MD simulations to evaluate the stability. GGND outperforms baseline models in both accuracy and stability under significant topological shifts, advancing stable molecular modeling for real-world applications.