High-order tensor neural network for iteration-free structure relaxation

Abstract

Structure relaxation is important for the discovery of new materials, yet conventional ab initio optimization remains a major bottleneck in high-throughput screening workflows. Machine learning potentials have accelerated relaxation by orders of magnitude, but they still rely on iterative optimization and high-quality DFT force labels. Here, we present HotRelax, a high-order tensor message-passing neural network for one-shot, end-to-end prediction of relaxed structures. Trained directly on paired unrelaxed and relaxed structures, HotRelax requires no DFT force labels and predicts relaxed structures in a single forward pass, without iterative inference or post-processing. Across five diverse datasets spanning 3D bulk crystals, 2D layered materials and catalysts, HotRelax shows strong performance relative to state-of-the-art end-to-end relaxation models, achieving lower prediction errors on several benchmarks while maintaining a compact model size and efficient inference. Extensive DFT calculations further show that the predicted structures are close in energy to their DFT-relaxed counterparts. When integrated into catalytic workflows, HotRelax also improves the accuracy and generalization of relaxed-state energy prediction models. Together, these results support HotRelax as an efficient and widely applicable framework for end-to-end structure relaxation, with strong potential to accelerate high-throughput materials discovery.