Learning Latent Design Spaces for Efficient Optimization of Pixelated Electromagnetic Structures

Pixelated electromagnetic (EM) structures offer substantial design flexibility, but their high-dimensional, combinatorial design spaces and costly full-wave simulations make target-driven optimization challenging. We investigate whether unsupervised representation learning can provide compact latent design spaces for efficient optimization of these structures. Engineering knowledge is encoded as geometric rules that generate large collections of layouts without EM response labels. We compare variational autoencoders, adversarial autoencoders, and an encoder-equipped Wasserstein generative model (WGAN-encoder) for learning low-dimensional representations of these geometric priors. Bayesian optimization then searches the learned spaces, using full-wave simulations to evaluate decoded candidates. We evaluate this pipeline on reflection metasurfaces (reflectarrays) and on-chip transformers, with four- and six-dimensional latent spaces, respectively. All three model families support effective downstream optimization, although convergence and final performance vary with the model and its regularization. A complete 16-cell reflection-phase library is obtained with 63 full-wave unit-cell evaluations and validated in a fabricated reflectarray, while transformer optimization improves the objective across all 16 target specifications. These results support learning from inexpensive geometric data as a practical approach to simulation-efficient optimization of pixelated EM structures across different representation models and device types.