Realizing weakly supervised learning by physical information for rapidly and accurately predicting three-dimensional weak electromagnetic field of metallic metasurfaces and zero-shot inverse design

This work introduces a separable, complex-valued 3D Maxwell loss function to physically constrain a 3D U-Net. This framework enables the prediction of complete vectorial electromagnetic fields for metallic metasurfaces across a broad spectral range, achieving a computational speedup exceeding two orders of magnitude (>100×) relative to the FDTD. A recognized limitation of purely data-driven networks is their inability to accurately predict weak field regions, which can even produce negative spectrum correlations. Incorporating Maxwell loss ensures accurate weak field predictions for absorptive materials. Additionally, this constraint allows effective weak supervision, reducing labeled points needed to just 12.5% of the total field points. More importantly, we have achieved zero-shot inverse design of meta-material structures for arbitrary materials and arbitrary geometries in three dimensions.