Surrogate Scattering Matrix-Guided Inverse Design of Nanophotonic Neural Networks

Optical computing offers a route to address the growing computational demands of machine learning, with inverse-designed nanophotonic media providing a compact path to passive optical operators. Training such devices end to end remains expensive because each geometry update requires full-wave forward and adjoint evaluations. We introduce a surrogate-guided inverse-design framework that separates task learning from electromagnetic realization. Classification is first solved in matrix space using a passive complex operator with bounded singular values, and the resulting target is transferred to a fabrication-aware freeform device through complex transmission matching and reflection suppression. Because the realization target is fixed, the electromagnetic work per update is determined by the input and output port counts and is independent of training-set size. A locality-constrained router composed with a fixed evanescent mixing stage extends the approach to 16-port transformations. Under the same physical initialization, solver, fabrication map, and 550-solve budget, operator matching reached 98.34% test accuracy on MedNIST, compared with 89.50% for direct geometry-to-task training. On RSSCN7, the combined optical surrogate reached 48.21%, compared with 38.57% for a PCA-16 ridge classifier. Three Yin-Yang realizations reached $91.44\pm 2.02$ %. These results establish surrogate-guided operator matching for compact, fabrication-aware photonic neural networks.