Enhanced posterior sampling via diffusion models for efficient metasurfaces inverse design

TL;DR

This paper tackles the challenging inverse design of metasurfaces, where nonlinear, high-dimensional mappings between geometry and electromagnetic response hinder traditional optimization. It proposes a diffusion-model framework augmented with a consistency loss and advanced posterior sampling (including posterior, Monte Carlo, and spherical Gaussian constrained variants) to ensure generated designs meet specified far-field requirements. The approach demonstrates state-of-the-art accuracy on small metasurfaces and introduces a scalable pipeline trained on $23\times23$ configurations that generalizes to large $98\times98$ arrays, achieving rapid design generation (about 2 minutes on an $A100$). By coupling a surrogate emulator with diffusion-based conditioning, the method provides robust, high-fidelity inverse designs suitable for practical metasurface fabrication and deployment.

Abstract

The inverse design of metasurfaces faces inherent challenges due to the nonlinear and highly complex relationship between geometric configurations and their electromagnetic behavior. Traditional optimization approaches often suffer from excessive computational demands and a tendency to converge to suboptimal solutions. This study presents a diffusion-based generative framework that incorporates a dedicated consistency constraint and advanced posterior sampling methods to ensure adherence to desired electromagnetic specifications. Through rigorous validation on small-scale metasurface configurations, the proposed approach demonstrates marked enhancements in both accuracy and reliability of the generated designs. Furthermore, we introduce a scalable methodology that extends inverse design capabilities to large-scale metasurfaces, validated for configurations of up to $98 \times 98$ nanopillars. Notably, this approach enables rapid design generation completed in minute by leveraging models trained on substantially smaller arrays ($23 \times 23$). These innovations establish a robust and efficient framework for high-precision metasurface inverse design.

Figures (16)

• Figure 1: Verification process of the inverse design flow using diffusion models.
• Figure 2: Final metric results for the three type of consistencies (no consistency loss, consistency loss and scheduled consistency loss) used during training. The results exhibit greater concentration near the optimal value when consistency loss is applied.
• Figure 3: $|$Far field$|$ after simulation from inverse-designed metasurface parameters using posterior sampling with 1k steps. Normalized guidance is defined as $q_t = \frac{1}{\|c - S_\phi(x_{0|t})\|_2}$, whereas non-normalized guidance corresponds to $q_t = 1$.
• Figure 4: Amplitude of the far field ($|$Far field$|$) obtained from inverse-designed metasurface parameters using Monte Carlo posterior sampling with $1,000$ steps and $N=10$. The normalized guidance is defined as $q_t = \frac{1}{\|c - S_\phi(x_{0|t})\|_2}$, while non-normalized guidance corresponds to $q_t = 1$.
• Figure 5: $|$Far field$|$ after simulation from inverse-designed metasurface parameters using Spherical Gaussian constrained Posterior Sampling.