The global shift towards renewable energy necessitates the development of ultrahigh-voltage (UHV) AC transmission to bridge the gap between remote energy sources and urban demand. While UHV grids offer superior capacity and efficiency, their implementation is often hindered by corona-induced audible noise (AN) and radio interference (RI). Since these emissions must meet strict environmental compliance standards, accurate prediction is vital for the large-scale deployment of UHV infrastructure. Existing engineering practices often rely on empirical laws, in which fixed log-linear structures limit accuracy and extrapolation. Herein, we present a monotonicity-constrained graph symbolic discovery framework, Mono-GraphMD, which uncovers compact, interpretable laws for corona-induced AN and RI. The framework provides mechanistic insight into how nonlinear interactions among the surface gradient, bundle number and diameter govern high-field emissions and enables accurate predictions for both corona-cage data and multicountry real UHV lines with up to 16-bundle conductors. Unlike black-box models, the discovered closed-form laws are highly portable and interpretable, allowing for rapid predictions when applied to various scenarios, thereby facilitating the engineering design process.