Molecular trajectory prediction is fundamental to computational chemistry, drug discovery, and materials simulation, enabling insights into dynamics, reaction pathways, and conformational stability. Its natural alignment with graph-structured spatiotemporal data has made it a key frontier in GNN research. However, current mainstream spatiotemporal GNNs, while enforcing E(3)-equivariance, treat atoms as unconstrained point masses and lack explicit rigid geometric constraints, often yielding unphysical deformations that compromise predictive interpretability. To address this challenge, we propose STEGMN—the first spatiotemporal graph architecture for molecular trajectory prediction that explicitly encodes rigid constraints. Inspired by Graph Mechanics Networks, we design a constraint-preserving equivariant spatiotemporal attention mechanism that captures temporal dependencies while rigorously maintaining both E(3)-equivariance and rigid-body constraints. Additionally, we introduce a constraint-preserving equivariant pooling module that generates future states by performing a learnable weighted aggregation of historical angular velocities, followed by forward kinematics mapping. This ensures that all outputs simultaneously satisfy E(3)-equivariance and strict bond-length conservation. Evaluated on real-world molecular dynamics datasets, STEGMN consistently outperforms strong baselines. On the rMD17 benchmark, it achieves an average ∼40% reduction in prediction MSE relative to representative spatiotemporal graph models (ST-GNN, ST-GCN, and ST-EGNN) across eight small-molecule systems, highlighting the critical value of explicit constraint modeling for physically stable trajectory prediction.
Miao et al. (Mon,) studied this question.