Optimizing Neural Networks for Nanophotonic Inverse Design Through Statistical and Computational Complexity Analysis

Optimizing neural networks (NNs) for inverse design in nanophotonics presents unique challenges due to the varying complexity of optical responses across different structures. This study introduces a machine learning-centric framework to systematically evaluate and optimize NN architectures based on both statistical and computational complexity. We assess statistical complexity through bias-variance tradeoff analysis, data efficiency, and latent space dimensionality using autoencoders, revealing how structural intricacy impacts generalization capacity. Computational complexity is analyzed through FLOPS, sparsity pruning, and convergence dynamics, offering insights into resource-efficient model deployment. Across multilayer films, metasurfaces, and gratings, we identify clear trends linking physical complexity to optimal model depth, width, and training regimes. Our findings highlight the importance of architectural tuning and model compression in achieving high accuracy with minimal computational overhead. This work provides a practical roadmap for designing interpretable, efficient, and scalable deep learning models tailored to complex physics-driven design problems.