Physics-guided Lorentzian sparse representation framework for accelerated parametric modeling of sparse S-parameters in MPCVD resonators

Microwave Plasma Chemical Vapor Deposition (MPCVD) is critical for high-quality diamond growth, and the resonant frequency of the cavity determines the energy efficiency and the plasma uniformity. Traditional design relies on full-wave simulations, which are time-consuming and experience-driven. AI-assisted methods have been used in microwave device modeling, but pole-residue neural networks have significant limitations for the sparse and sharp S-parameters of high-Q MPCVD cavities: fitting the flat background requires a large number of redundant poles, which inflates the model order and degrades the efficiency, and the coexistence of resonant and background poles causes parameter jumps that reduce the robustness. This paper proposes a physics-informed sparse representation (PISR) method. It builds a Lorentzian basis matching the resonant mode shapes and compresses the high-dimensional S-parameters into a low-dimensional set of physical features: resonance frequencies, amplitudes and Q-factors. A three-stage neural network is designed: a classification net predicts the number of resonance peaks, a regression net determines their frequencies under the predicted peak count, and a further regression net learns the Lorentzian parameters. The reduction from the reflection coefficient to the Lorentzian line-shape is established rigorously: the poles and residues of 𝑆11 are obtained in closed form including the port loading, the approximation error is shown to equal an out-of-quadrature residual that vanishes exactly at every resonance, and a closed-form bound is proved for the line-shape flanks (κ²/8 in the weakly coupled limit, rising to κ²/2 at critical coupling) and verified numerically. On a 1500-sample MPCVD dataset the peak-count accuracy is 1.000, the reconstructed S-parameters closely match the full-wave simulations with a single-sample end-to-end mean-squared error of 1.54 × 10^-4 dB², more than two orders of magnitude lower than the pole-residue space-mapping approach (3.72 × 10^-2 dB²), and the training time is greatly shortened. These results demonstrate that PISR offers superior accuracy and stability, higher efficiency and strong physical interpretability.