DoMiNO: Decomposing Molecular Dynamics with Multi-Scale Neural Graph Ordinary Differential Equations

Molecular dynamics (MD) simulations are crucial for understanding and predicting the behavior of molecular systems in biology and chemistry. Yet, predicting long-term dynamics is still challenging. On one hand, it is hard to employ small-timestep models for long-term prediction, due to substantial rollout errors accumulated at each step, not to mention their extremely high time complexity due to the large number of rollout steps. On the other hand, it is hard to use large-timestep models to achieve high accuracy, due to their inability to capture subtle details of the dynamics. To bridge this dichotomy, we propose DoMiNO , a multi-scale framework that decomposes MD dynamics into several temporal resolutions, each governed by a neural graph ordinary differential equation (GraphODE) and are adaptively fused for final predictions. Concretely, DoMiNO  operates through three key components: (1) an E(n)-equivariant graph neural network (EGNN) encoder that initializes latent states from a single observed molecular structure, maintaining SE(3) symmetries throughout; (2) a hierarchy of GraphODEs where each level captures scale-specific dynamics over normalized local time intervals, ranging from slow global motions to fast bond vibrations; and (3) an attention-based fusion module that adaptively combines multi-level predictions and reconstructs SE(3)-equivariant 3D coordinates. This design enables each hierarchical level to specialize in its characteristic timescale while preserving molecular symmetries. During inference, DoMiNO  flexibly assembles predictions across different temporal resolutions, providing superior performance over both short-term and long-term dynamics. Empirical results on challenging MD benchmarks demonstrate that DoMiNO  achieves significant improvements in prediction accuracy, particularly for molecules with pronounced timescale separation. The method exhibits significantly slower error growth over extended horizons compared to both single-scale baselines and state-of-the-art multi-step approaches. Our implementation is available at https://github.com/FrancoTSolis/DoMiNO-TKDD-Code .