Discovering governing equations for transmission line is essential for the study on its properties, especially when the nonlinearity is introduced in a transmission line system. In this paper, we propose a novel data-driven approach for deriving the governing partial differential equations based on the spatial-temporal samples of current and voltage in the transmission line system. The proposed method is based on the ridge regression algorithm to determine the active spatial differential terms from the candidate library that includes nonlinear functions, in which the time and spatial derivatives are estimated by using polynomial interpolation. Three examples, including uniform and nonuniform transmission lines and a specific type of nonlinear transmission line for soliton generation, are provided to benchmark the performance of the proposed approach. The results demonstrate that the newly proposed approach can inverse the distributed circuit parameters and also discover the governing partial differential equations in the linear and nonlinear transmission line systems. Our proposed data-driven method for deriving governing equations could provide a practical tool in transmission line modeling.
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