Traj2Relax: A Trajectory-Supervised Method for Robust Structure Relaxation

Structure relaxation plays a crucial role in atomic simulation and materials modeling, yet traditional first-principles approaches remain computationally expensive and, therefore, difficult to scale to high-throughput applications. In this work, we propose <b>Traj2Relax</b>, a trajectory-supervised structure relaxation framework based on conditional velocity field modeling. Instead of relying on explicit energy or force evaluations, Traj2Relax learns a time-dependent velocity field from geometric differences between successive configurations along real relaxation trajectories, enabling physically consistent structural convergence across a wide range of perturbation magnitudes. A time-scheduled noise mechanism is introduced during training to improve stability under highly distorted inputs, while deterministic integration during inference produces smooth, interpretable relaxation trajectories. Experimental results show that Traj2Relax achieves competitive accuracy under near-equilibrium conditions and demonstrates clear advantages under moderate to strong perturbations, where energy-driven and distribution-based relaxation methods tend to degrade. On representative inorganic crystal systems, Traj2Relax attains a root-mean-square deviation of 0.26 Å and a space-group consistency of 82.3% under equilibrium settings and maintains a root-mean-square deviation of 0.38 Å with a recovery rate of 5.8% under strong perturbations. The framework further supports deterministic, batch-parallel relaxation, yielding an order-of-magnitude improvement in inference throughput compared with iterative energy-minimization-based approaches. Overall, Traj2Relax provides an efficient and physically grounded alternative for learning-driven structure relaxation, particularly suited for high-throughput screening scenarios involving nonequilibrium or highly perturbed structures.