Abstract:Physics-informed operator learning methods (e.g., PI-DeepONet), while advantageous for accelerating the solution of partial differential equations (PDEs), face challenges of high training costs in high-order problems due to limitations of automatic differentiation. To address this, a novel prediction-differential decoupled neural network architecture, UNet-RBF, is proposed. It employs U-Net as the prediction network to extract spatial features of PDE parameters and utilizes a lightweight Radial Basis Function (RBF) network as the differential network to impose physical constraints. By freezing the RBF network parameters during training, the prediction task is decoupled from differential computation, significantly reducing the computational overhead of automatic differentiation. Numerical experiments demonstrate that UNet-RBF substantially improves the training efficiency and stability for solving high-order PDEs while maintaining high prediction accuracy (relative error less than 1%). Compared to the traditional PI-DeepONet, the training efficiency for fourth-order problems is increased by over 1500%, and the model exhibits stronger robustness, offering an effective pathway for the rapid and accurate solution of complex physical problems.