Discovering Explicit Magnetic Core Loss Equations via Learnable Symbolic Sparse Identification

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.