Magnetic core loss—the energy wasted as heat in transformer cores and other magnetic devices—is a critical design consideration for high-frequency power electronics. Engineers have long relied on the Steinmetz Equation, an empirical formula developed over a century ago, to estimate these losses during equipment design. However, this traditional approach sacrifices accuracy, while modern neural network solutions improve predictions but become computational black boxes that designers cannot easily interpret or trust.
A new research team has introduced LSSI, a symbolic regression framework that bridges this gap. Rather than fitting arbitrary neural networks or applying rigid historical equations, LSSI automatically discovers simple, mathematically explicit equations directly from experimental data. The method works by expanding the traditional Steinmetz library of candidate mathematical functions, then intelligently selecting which terms matter most while simultaneously optimizing their exponents and coefficients as learnable parameters.
The results are striking. Testing on real magnetic core data, LSSI achieved R² accuracy of 0.9999 with a mean absolute percentage error of just 1.04%—exceeding both classical and modern machine learning approaches. Critically, the discovered equations contain only four active mathematical terms and require just 15 parameters to implement, compared to 4,417 parameters in equivalent neural network models.
This compactness matters enormously for practical engineering. Designers can implement these equations in spreadsheets, embedded firmware, and real-time control systems without computational burden. The explicit mathematical form also makes the underlying physics transparent, enabling engineers to understand trade-offs and validate results against physical intuition.
For the power industry, LSSI promises faster, more confident design of magnetic components ranging from distribution transformers to switched-mode power supplies. The framework could accelerate development of more efficient, compact equipment while reducing reliance on expensive, time-consuming laboratory characterization.
