Abstract: To address computational bottlenecks in metasurface optimization, we proposed a GMN-driven intelligent operator surrogate framework. We developed a unified near- and far-field model based on GMN that predicted fields via S-parameter matrices, effective excitations, and angular-spectrum propagation. We then built a physics-guided Fourier Neural Operator (FNO) surrogate to learn the operator mapping from port configurations to field distributions, embedding angular-spectrum propagation and physical constraints. On a 20×20 PIN-diode metasurface with eight-spot focusing, GMN agreed with HFSS and provided reliable training data. The trained FNO now achieves a 40,000× memory reduction and a 2000,000× speedup over HFSS, with near-field errors below 3% and power-conservation error below 5%. These results indicate that GMN enables a learnable operator representation and that FNO provides efficient spectral-convolution approximations suitable for real-time metasurface optimization.