基于可学习符号稀疏识别的显式磁芯损耗方程发现
Discovering Explicit Magnetic Core Loss Equations via Learnable Symbolic Sparse Identification
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中文总结 AI 辅助
该研究针对磁芯损耗方程精度与物理可解释性难以兼顾的问题，提出LSSI框架，构建了仅含4项的紧凑显式方程，实现0.9999的R²值与1.04%的MAPE，大幅降低参数规模，兼具精度与物理可解释性。
中文摘要 AI 辅助
具有简单表达式和物理可解释性的显式磁芯损耗方程是高频功率磁元件设计中的重要工具。传统对经验数据的拟合（如斯坦梅茨方程（Steinmetz Equation, SE））往往难以保证精度，而现代机器学习方法虽能提升预测精度，却违背了物理规律。为填补这一空白，本文提出一种用于数据驱动方程发现的可学习符号稀疏识别（Learnable Symbolic Sparse Identification, LSSI）框架。具体而言，LSSI将正弦驱动下的磁芯损耗方程重新构建为直接从实验数据推导的符号回归问题；在斯坦梅茨方程的基础上，引入扩展的候选函数库，并采用稀疏识别框架筛选主导函数；更重要的是，将候选函数的指数、系数等关键参数设为可学习参数，同时实现方程简洁性与潜在分数幂律的高表达性。实验结果表明，LSSI通过仅含4个有效项的高度紧凑显式方程，达到了0.9999的最优R²值和1.04%的平均绝对百分比误差（MAPE），且将参数数量从神经网络方法的4417个大幅减少至15个，展现出卓越的紧凑性与效率。因此，LSSI框架为复杂现代磁特性表征与设计提供了一种物理透明且精度极高的解决方案。
英文摘要
Explicit magnetic core loss equations with simple expressions and physical interpretability are significant tools in the design of high-frequency power magnetics. Traditional fits to empirical data like the Steinmetz Equation (SE) often struggle with accuracy, whereas modern machine learning approaches improve precision but deviate from physics. To fill this gap, this paper proposes a Learnable Symbolic Sparse Identification (LSSI) framework for data-driven equation discovery. Specifically, LSSI reformulates magnetic core loss equations for sinusoidal drives as a symbolic regression problem derived directly from experimental data. Building upon the SE, an expanded library of candidate functions are introduced and a sparse identification framework is implemented to select the dominant ones. More importantly, crucial parameters like exponents and coefficients of candidate functions are treated as learnable ones, simultaneously achieving equation simplicity and high expressiveness of the underlying fractional power laws. Experimental results demonstrate that LSSI achieves superior accuracy with a state-of-the-art $\mathbf{R^2}$ of $\mathbf{0.9999}$ and a MAPE of $\mathbf{1.04\%}$ through a highly compact explicit equation containing only $\mathbf{4}$ active terms. Furthermore, it drastically reduces the parameter count from $\mathbf{4417}$ in neural network methods to $\mathbf{15}$, showcasing exceptional compactness and efficiency. The LSSI framework thus provides a physically transparent and highly accurate solution suitable for complex modern magnetic characterization and design.
