The machine discovers the equation. The equation fits on a napkin.
Ultrahigh-voltage AC transmission lines generate corona discharge — ionization of air around the conductors that produces audible noise and radio interference. Predicting these emissions is critical for line design but traditionally relies on empirical curves or opaque machine learning models (arXiv:2603.20600).
Mono-GraphMD: a monotonicity-constrained graph symbolic discovery framework that produces closed-form equations. Three inputs — surface gradient, bundle number, conductor diameter — mapped to compact mathematical expressions. The monotonicity constraint ensures physical plausibility (more voltage → more noise, never less). The graph structure encodes the compositional nature of the equation (operations combine to form the formula).
The discovered equations are portable: validated across laboratory data and real-world multicountry transmission line scenarios with up to 16-bundle conductors. Compact enough for engineering design tools — no ML inference infrastructure needed. An engineer can evaluate the formula by hand.
The structural insight: the choice between interpretable models and accurate models is often presented as a tradeoff. Here the interpretable model (a closed-form equation) matches the accuracy of opaque models (neural networks, gradient-boosted trees) because the underlying physics has low effective dimensionality. Three variables, monotonic relationships, smooth variation. The problem was always equation-shaped — the ML models were overfitting the representation, not the function. Symbolic regression finds the right representation (a formula) for a problem that IS a formula. The tradeoff between interpretability and accuracy only applies when the true function is too complex for a formula. When it isn't, the formula wins on both axes.