FORK: First-Order Relational Knowledge Distillation for Machine Learning Interatomic Potentials

State-of-the-art equivariant Graph Neural Networks (GNNs) achieve quantum-level accuracy for molecular simulations but remain computationally prohibitive for large-scale applications. Knowledge distillation (KD) presents a solution by compressing these GNN-based Machine Learning Interatomic Potentials (MLIPs) into efficient models, yet existing distillation methods fail to capture the physics. Current KD approaches rely on simplistic atom-wise feature matching, overlooking the core physical principle of interatomic interactions that define the potential energy surface (PES). We introduce FORK, First-Order Relational Knowledge Distillation, a framework that distills relational knowledge from pretrained GNNs by modeling each interatomic interaction as a relational vector. Through a contrastive objective, FORK guides compact student models to preserve the geometric structure of the teacher's learned PES. On the OC20 and SPICE benchmarks, our FORK-trained student outperforms baselines in energy and force prediction, achieving faithful physical knowledge transfer at a fraction of the computational cost.In a practical high-throughput catalyst screening application, the distilled model achieves a 11.9× acceleration while preserving chemical coherency, validating its efficacy for accelerating large-scale materials discovery.