AI 中文总结
本研究针对永磁体建模的核心问题，通过12012组微磁学模拟数据训练机器学习模型，结合符号回归得到闭式表达式，还发布了mammos-ai包实现快速参数筛选，提升了预测效率与精度。
AI 中文摘要
从磁畴的磁滞回线预测其外在性能（即矫顽力、剩余磁化强度和最大磁能积）是永磁体建模中的核心问题，需结合其内在微磁学参数。成熟的分析模型虽能提供有用估计，但常忽略非均匀磁化过程，而直接微磁学模拟计算成本高昂。本研究基于12012个理想立方磁畴的微磁学模拟数据训练机器学习模型，覆盖饱和磁化强度、交换常数和单轴各向异性常数的宽范围取值。在相同的保留测试数据上与分析模型对比，机器学习模型预测上述三种外在性能的误差显著更低。符号回归恢复了矫顽力的Kronmüller形式，其中有效退磁因子依赖于材料，还得到了剩余磁化强度和最大磁能积的新闭式表达式。每个公式最多含两个拟合常数，却达到了机器学习模型的精度。本研究还探究了从三种外在参数反推内在参数的逆问题：饱和磁化强度和各向异性常数可被准确恢复，而交换常数无法准确恢复，因其对外在性能的影响较弱。训练好的模型通过mammos-ai Python包发布，可在数秒内筛选数千个候选参数集，而直接微磁学模拟需耗时数小时至数天。
英文摘要
Predicting the extrinsic properties from hysteresis loops of a magnetic grain, namely the coercive field, remanent magnetisation, and maximum energy product, from its intrinsic micromagnetic parameters is a central problem in permanent-magnet modelling. Established analytical models provide useful estimates but often neglect nonuniform magnetisation processes, whereas direct micromagnetic simulations are computationally expensive. In this work, we train machine-learning models on 12012 micromagnetic simulations of an idealised cubic grain, spanning broad ranges of the saturation magnetisation, exchange constant, and uniaxial anisotropy constant. Benchmarked against the analytical models on identical held-out data, the machine-learning models predict all three extrinsic properties with substantially lower errors. Symbolic regression recovers the Kronmüller form of the coercive field, with an effective demagnetising factor that depends on the material, and finds new closed-form expressions for the remanence and maximum energy product. Each law contains at most two fitted constants yet approaches the accuracy of the machine-learning models. We also investigate the inverse problem of recovering the intrinsic parameters from the three extrinsic properties. The saturation magnetisation and anisotropy constant are recovered accurately, whereas the exchange constant is not, because it influences the extrinsic properties only weakly. The trained models are released through the mammos-ai Python package, enabling thousands of candidate parameter sets to be screened in seconds rather than the hours or days required by direct micromagnetic simulation.
Comments14 pages, 9 figures, 3 tables. Supplementary material (8 pages, 11 figures, 8 tables) included as an ancillary file
