Topology-Aware Dimensionless Modeling of Resonance Frequency in Square-Loop and Cross Conductive Metasurfaces

Periodic conductive metasurfaces provide a compact means of controlling frequency-selective electromagnetic transmission and shielding; however, their design is commonly performed using topology-specific parametric optimization, limiting the transferability of design knowledge across different unit-cell geometries. This study develops a topology-aware dimensionless scaling framework for square-loop and cross periodic conductive patterns supported by dielectric substrates. A spectral-domain surface-current method-of-moments solver was formulated using a zero-thickness sheet-admittance representation and validated through convergence tests and published full-wave benchmark cases, yielding a mean absolute resonance-frequency deviation of approximately 0.48%. A 162-case factorial dataset was then generated by independently varying normalized resonator size, conductor width, substrate thickness, and relative permittivity. An initial validation comparison showed that introducing a compact topology-dependent correction reduced the normalized-resonance RMSE from 0.05165 for the topology-blind model to 0.00504. Repeated paired nested cross-validation further demonstrated that the compact M2 model achieved a mean RMSE of 0.00518, while the fully topology-specific M3 model provided the lowest error of 0.00351. These findings quantify the trade-off between predictive accuracy and topology-dependent model complexity. Dense geometry and substrate validation sweeps further confirmed low prediction errors, with mean absolute errors below 0.52% across all evaluated cases. The results show that canonical conductive metasurfaces exhibit a common low-dimensional electromagnetic trend, while accurate cross-topology prediction requires only a limited topology-dependent correction. The proposed framework provides a compact and interpretable approach for topology-aware resonance-frequency prediction within the investigated conductive metasurface design space.