用深度学习逆向设计微波滤波器，大幅减少仿真时间。

Designing high-performance substrate-integrated waveguide (SIW) filters with both closely spaced and widely separated resonances is challenging. Consequently, there is a growing need for robust methods that reduce reliance on time-consuming electromagnetic (EM) simulations. In this study, a deep learning-based framework was developed and validated for the inverse design of multi-mode SIW filters with both closely spaced and widely separated resonances. A series of SIW filters were designed, fabricated, and experimentally evaluated. A three-stage deep learning framework was implemented, consisting of a Feedforward Inverse Model (FIM), a Hybrid Inverse-Forward Residual Refinement Network (HiFR\textsuperscript{2}-Net), and an Iterative Residual Correction Network (IRC-Net). The design methodology and performance of each model were systematically analyzed. Notably, IRC-Net outperformed both FIM and HiFR\textsuperscript{2}-Net, achieving systematic error reduction over five correction iterations. Experimental results showed a reduction in mean squared error (MSE) from 0.00191 to 0.00146 and mean absolute error (MAE) from 0.0262 to 0.0209, indicating improved accuracy and convergence. The proposed framework demonstrates the capability to enable robust, accurate, and generalizable inverse design of complex microwave filters with minimal simulation cost. This approach is expected to facilitate rapid prototyping of advanced filter designs and could extend to other high-frequency components in microwave and millimeter-wave technologies.