LSSI framework discovers compact magnetic core loss equations with 0.9999 R²

Designing high-frequency power magnetics relies on accurate magnetic core loss equations. Traditional empirical fits like the Steinmetz Equation (SE) often fail to capture complex behavior, while modern neural network models boost accuracy at the cost of physics interpretability. To bridge that gap, the authors from arXiv introduce LSSI, a Learnable Symbolic Sparse Identification framework that reformulates core loss modeling as a symbolic regression problem. It builds on the Steinmetz equation by expanding a library of candidate functions, then applies sparse identification to pick only the most dominant terms. Crucially, the exponents and coefficients of those terms are treated as learnable parameters, letting the method find fractional power laws without sacrificing simplicity.

LSSI achieves a state-of-the-art R² of 0.9999 and a mean absolute percentage error (MAPE) of only 1.04%, using a highly compact explicit equation with just 4 active terms. That's a dramatic reduction from 4417 parameters required by neural network approaches, down to 15. The result is a physically transparent, interpretable equation that maintains high accuracy across complex modern magnetic characterization. This could enable engineers to build more efficient power converters and high-frequency magnetics without manually tuning empirical formulas, offering a practical pathway for data-driven design in power electronics.