Materials with perovskite phases are widely used in solar cells and ferroelectric, piezoelectric, dielectric and superconducting devices due to their various notable functions. However, structural instability limits some compositions in forming robust perovskite phases for device applications. The analytical approach using the tolerance factor (t) can only guarantee prediction accuracy within a limited range, ascribed to its nature of overlooking the atomic interaction. Hence, here we establish a prediction model using formation energy as the target parameter for its reflection of the reaction of atoms and apply machine learning as the analysis method since it has been successfully employed in plenty of material property prediction studies. Machine learning employs statistical methodologies to identify correlative patterns within large-scale datasets, enabling accurate predictions with robust generalization. In this work, we built a model to predict the formation energy of ABX₃ perovskite using machine learning and achieved a model with an R-squared value of 0.928 and a root mean square error of 0.301 eV/atom, validated by first-principles computations. In total, 75% of the values were correctly predicted within an error lower than 0.06. This work could contribute to accelerating the study of solving perovskites’ instability.

In the current Industrial Internet of Things (IIoT) environment, data security for product lifecycle management is greatly challenged, particularly in scenarios involving vertical multi-level Bill of Materials (BOM) deep nesting and lifecycle dynamic evolution. The traditional case-bounding model, in large-scale deployment, easily leads to rule expansion and an increase in database I/O overhead, thus causing authorization lag, authority boundary ambiguity and other problems. To address these limitations, this paper proposes a Decoupled Hybrid Access Resolution (DHAR) framework. The framework separates static organizational roles from dynamic lifecycle constraints, and the complexity of authorization configuration is reconstructed from case-dependent growth into an object-instance-independent bounded structure; combined with the state-based pre-filtering mechanism and memory cache strategy, redundant recursive query is reduced. Experiments on increasing BOM depths show that, under a 20-layer topology, DHAR reduces average access latency from 285.8 ms to 1.3 ms. Under a 20-layer BOM with 1000 concurrent requests, DHAR maintains an average latency of 5.2 ms, while compressing the authorization rule set from millions to hundreds. These results indicate that, within the studied vertical multi-level BOM setting, DHAR improves response performance while preserving data consistency and strengthening protection against unauthorized modification.