ASPIRE: Saddle-Point Discovery through Set Prediction and Physical Refinement

Yucheng Zhao, Quanyou Zhang, Shaoxiang Qin, Haixuan Xu, Xiongye Xiao

Predicting thermally activated diffusion and defect evolution with event-driven models requires identifying atomic rearrangement mechanisms and their activation barriers. Discovering the associated saddle points is a major computational bottleneck: multiple rearrangements may originate from one metastable state, while costly local searches can fail or repeatedly converge to the same saddle. To address this challenge, we introduce ASPIRE (Atomistic Saddle-Point Inference with Refinement for Events), a framework that predicts a set of saddle candidates from a single initial atomic environment and refines them through Dimer searches on the original interatomic potential. The framework's equivariant set predictor, Ev-Quiformer, integrates (i) geometry-conditioned scalar-vector event slots for generating multiple saddle-point proposals and (ii) a decoder that maps each slot to a full atomic displacement field by combining atom, slot, and anchor-relative vectors with invariant coefficients. We also contribute two datasets: (i) BCCFE4VACAV-4000, comprising 4,000 four-vacancy body-centered cubic iron configurations and 65,450 reference events grouped by initial state for set supervision…