Physics-informed conditional diffusion for inverse design of MRI metamaterials

Inverse design of magnetic resonance imaging (MRI) metamaterials is a physics-constrained design problem with sharp spectral targets, expensive full-wave simulation, and multimodal parameter-to-response mappings. We study a six-parameter cylindrical MRI metamaterial and solve its inverse design with a two-stage neural workflow. The forward surrogate Physics-prior-enhanced Lorentzian-parameterized Regression Network (PLRNet) combines a multi-peak asymmetric-Lorentzian head with a learned residual, reaching 0.23 MHz frequency mean absolute error (MAE) and Spearman ρ=0.99 for field-strength ranking. A scalar-conditioned diffusion model with classifier-free guidance samples designs from [f_target,R_geo,B_score] and reaches 0.11 MHz MAE across eight test conditions covering 1.5 T/3.0 T and 50-150 mm radii. Full-wave verification in Computer Simulation Technology (CST) Microwave Studio across all eight conditions gives 0.49 MHz MAE, 69% below cGAN at 1.57 MHz, and 78% below cVAE at 2.21 MHz under matched parameter counts. The generated high-performance designs favor low unit-cell count N and capacitance values consistent with the lumped inductor-capacitor resonance constraint.