Data-Driven Discovery of the Governing Equation for the Transmission Lines System

Sophisticated structures in the transmission line system introduce the nonuniformity and nonlinearity, which brings the challenge for its characterization and modeling. In this work, a novel data-driven method is proposed to derive the governing partial differential equations of the transmission line. Based on the polynomial interpolation of the spatialtemporal samples of current and voltage, the time and spatial derivatives can be obtained. Then, the ridge regression algorithm is adopted to determine the active spatial differential terms from the candidate functions. Three benchmarks, the uniform and nonuniform transmission line, and a soliton generation system, are provided to demonstrate the validity of the newly proposed approach.