Physics-Informed Mixture Density Network Architecture for Inverse Design of Substrate Integrated Coaxial Line

To address the challenges of the 'one-to-many' mapping ill-posedness and the prohibitive computational cost of traditional optimization methods in the inverse design of high-frequency Substrate Integrated Coaxial Line (SICL), this paper proposes a Physics-Informed Mixture Density Network (PI-MDN) inverse design architecture. This method reformulates deterministic regression into the estimation of the conditional probability density function of design parameters. By explicitly embedding geometric hard constraints and physical repulsive loss into the feature space, it effectively decouples the nonlinear dependencies of multimodal solutions. Based on the physics-aware constraint mechanism and dynamic learning rate scheduling, the model achieves a significant performance breakthrough on a broadband validation set, with a coefficient of determination (R²) of 0.9708 and a Mean Absolute Percentage Error (MAPE) reduced to 2.80%. Experimental results demonstrate that this framework not only effectively overcomes the geometric sensitivity challenges in high-impedance regions but also provides a high-fidelity, real-time automated inverse design scheme for precision RF/microwave circuits while strictly satisfying micronano fabrication process constraints.