Abstract: The computation of electromagnetically induced multiphysics plays a crucial role in the design of high-power microwave devices. To rapidly and accurately obtain the multiphysics responses induced by electromagnetic fields in high-power cavity filters, this paper proposes a data-driven surrogate model. Specifically, we first build a multiphysics response database for cavity filters by using the finite element method. Subsequently, we develop a data-driven artificial neural network surrogate model based on this database. The result comparison demonstrates that the surrogate model can accurately and fast predict the S-parameter curves of high-power cavity filters under different input powers, with a prediction accuracy exceeding 98% and a prediction time of less than 0.2 s. Compared to traditional numerical computations of electromagnetically induced multiphysics, the computational speed is improved by more than three orders of magnitude. Therefore, the fast and accurate prediction capability of this innovative surrogate model holds significant implications for the stability analysis, reliability assessment, and optimization design of novel high-power microwave devices.