PearSAN: an inverse design framework for the latent optimization of photonic devices using Pearson Correlated Surrogate Annealing

High-dimensional optimization problems represent a significant challenge in many physics-based design tasks due to the vast size of the search spaces. Consequently, latent optimization methods have emerged as a viable solution, reducing the dimensionality of the search space while preserving key design features. In this work, we improve upon current latent optimization methods for inverse design by introducing PearSAN (Pearson Correlated Surrogate Annealing), a novel machine learning optimization algorithm that trains a latent surrogate function to guide latent sampling. The core innovation of PearSAN is the Pearson Correlated Surrogate Optimization Loss (PearSOL), which enforces a monotonic relationship between the surrogate function and the figure of merit (FOM) of designs. Unlike traditional energy-matching techniques, which can lead to suboptimal alignment with sampling methods, PearSOL ensures that the surrogate function more accurately guides the exploration of the latent space. When applied to the optimization of metasurfaces, PearSAN's sampling procedure achieved an average FOM of ~92%, vs. ~80% achieved in the previous latent optimization framework. Furthermore, our model generates designs several orders of magnitude faster than previous frameworks, only requiring ~10 seconds per 100 designs. Our findings demonstrate PearSAN's potential to dramatically improve the efficiency and accuracy of generative design tasks in high-dimensional physics-based systems.