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

2026-10-07

AI Summary

This study addresses the computational bottlenecks in saddle point search for atomic diffusion and defect evolution, where conventional methods frequently suffer from entrapment in local extrema and redundant convergence. To this end, we propose ASPIRE, a novel framework that introduces a geometry-conditioned scalar-vector event slot mechanism. Leveraging the equivariant set predictor Ev-Quiformer, ASPIRE generates multiple saddle point candidates in parallel from initial atomic environments, supported by theoretical guarantees of proposal equivariance, which are subsequently refined via the Dimer method. Experimental results demonstrate that ASPIRE achieves an event coverage rate of 77.20%, outperforming existing baselines. Furthermore, it reduces Dimer force evaluations by half and decreases per-configuration computation time from 478.8 to 176.3 seconds, significantly enhancing the efficiency of saddle point discovery.

Abstract

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 and post-refinement evaluation; and (ii) BCCFE-1TO4VAC, comprising 5,372 configurations with one to four vacancies each. Theoretically, we establish conditions for proposal equivariance. Experimentally, ASPIRE achieves 77.20% reference-event coverage on this benchmark, compared with 75.73% for a conventional Dimer baseline, while requiring approximately half as many Dimer force evaluations. In a timing evaluation on 50 configurations, ASPIRE reduces wall time per configuration from 478.8 s to 176.3 s under the stated hardware settings.

Problem

• saddle-point discovery
• activation barriers
• atomic rearrangement mechanisms
• event-driven models
• computational bottleneck

Innovation

• Saddle-point prediction
• Equivariant set prediction
• Ev-Quiformer
• Defect evolution
• Dimer refinement