Ultra-fast inverse design of an on-chip diffractive optical neural network via two-step decomposition

Inverse design of on-chip diffractive optical neural networks (DONNs) commonly relies on full-wave simulation-in-the-loop optimization, which becomes prohibitively expensive as the dataset size and the number of device degrees of freedom increase. In this work, we present a two-step decomposition method (TSDM) to accelerate this process. The methods combine a neural surrogate solver, trained on spatially decoupled metasurface patches to predict layer-wise field modulation, together with a linear decomposition of multi-port excitations into single-port response bases. This reduces the number of solver calls from the dataset size to the number of input ports. The surrogate model is trained on 73,000 input-structure pairs and achieves a mean square error of 0.004 compared with 3D FDTD simulations. We further demonstrate inverse-designed DONNs for the Iris and MNIST classification, with accuracies of 93.33% and 91.86%, respectively. The MNIST design is completed in 0.72 hours on a single GPU, corresponding to a 22.8 times speedup over a neural-surrogate baseline and hundreds-fold acceleration compared to direct FDTD adjoint optimization. The proposed framework provides an efficient and scalable approach for designing large-scale on-chip optical computing systems.