Diffusion Schrödinger Bridges with enhanced posterior sampling for metasurface inverse design

Abstract

Metasurface inverse design is challenged by the intricate relationship between structural parameters and electromagnetic responses, as well as the high dimensionality of the optimization space. Local models, while commonly employed, quickly become infeasible for complex and locally coupled structures. Conventional iterative optimization techniques, on the other hand, are computationally intensive, time-consuming, and susceptible to convergence in local minima. This study explores a versatile generative methodology based on enhanced posterior sampling within the Schrödinger Bridge framework. By decomposing posterior sampling into amplitude and directional contributions, we effectively integrated different kind of posterior sampling. This approach is further supported by refined training strategies to enhance performance and reduce the complexity of hyperparameter optimization. The proposed framework demonstrates exceptional accuracy and robustness, representing a significant advancement in metasurface design. Notably, it enables high-precision inverse design for large-scale configurations of up to $350 \times 350$ pillar arrays, despite being trained on significantly smaller arrays of $23 \times 23$ pillars.

Figures (33)

• Figure 1: Validation workflow for the inverse design pipeline employing DSBs.
• Figure 2: Final performance metrics are compared with and without score conditioning. Models employing conditional scores demonstrate superior results.
• Figure 3: The $R^2$ metric, computed after simulation of inverse-designed metasurface parameters using Spherical Gaussian Constrained Posterior Sampling, is evaluated for varying magnitudes of the diversity coefficient $\alpha$. Remarkably, the $R^2$ remains high even at low values of $\alpha$ and stays stable until the gradient-based guidance contributes less than half to the overall update.
• Figure 4: a) $R^2$ values for DSBs using direction and amplitude-constrained posterior sampling. b) Comparative performance analysis of amplitude-constrained posterior sampling between DSBs and DMs.
• Figure 5: Spectrum of the Hessian for the three highest-performing and three lowest-performing posterior sampling schemes under direction constraints, amplitude constraints, and their combined application.