Improving conditional generative adversarial networks for inverse design of plasmonic structures

TL;DR

This work addresses the challenge of inverse design for plasmonic nanostructures by enhancing conditional GANs with two targeted improvements: label projection in the critic and a label embedding network. Evaluated on two architectures (FCGAN and DCGAN) and guided by a surrogate forward model, the approach achieves substantially lower spectrum MAEs and faster convergence, demonstrating improved efficiency for designing optical elements from extinction spectra. The results indicate that the proposed modifications help navigate the one-to-many nature of inverse design while maintaining accuracy, with practical implications for rapid, high-fidelity nanophotonic design. Overall, the study advances efficient inverse design methods for plasmonic structures using GW-based conditioning and surrogate evaluation.

Abstract

Deep learning has emerged as a key tool for designing nanophotonic structures that manipulate light at sub-wavelength scales. We investigate how to inversely design plasmonic nanostructures using conditional generative adversarial networks. Although a conventional approach of measuring the optical properties of a given nanostructure is conceptually straightforward, inverse design remains difficult because the existence and uniqueness of an acceptable design cannot be guaranteed. Furthermore, the dimensionality of the design space is often large, and simulation-based methods become quickly intractable. Deep learning methods are well-suited to tackle this problem because they can handle effectively high-dimensional input data. We train a conditional generative adversarial network model and use it for inverse design of plasmonic nanostructures based on their extinction cross section spectra. Our main result shows that adding label projection and a novel embedding network to the conditional generative adversarial network model, improves performance in terms of error estimates and convergence speed for the training algorithm. The mean absolute error is reduced by an order of magnitude in the best case, and the training algorithm converges more than three times faster on average. This is shown for two network architectures, a simpler one using a fully connected neural network architecture, and a more complex one using convolutional layers. We pre-train a convolutional neural network and use it as surrogate model to evaluate the performance of our inverse design model. The surrogate model evaluates the extinction cross sections of the design predictions, and we show that our modifications lead to equally good or better predictions of the original design compared to a baseline model. This provides an important step towards more efficient and precise inverse design methods for optical elements.

Figures (10)

• Figure 1: This schematic presents an overview of the inverse design framework presented in this work. a) We train a cGAN-model consisting of a generator and a critic network, to predict optimal designs of dimer structures. Based on the desired cross-section spectra $\mathbf{y}$, and a stochastic vector $\mathbf{z}$, the generator learns to predict the design $\mathbf{\tilde{x}}$. The critic network provides feedback to the generator by estimating the statistical distance between the original design $\mathbf{x}$ and $\mathbf{\tilde{x}}$ produced by the generator. The model is empirically optimized to minimize the statistical distance between samples, using simulation data. Training is stopped when the distribution of $\mathbf{\tilde{x}}$ has converged to the distribution of $\mathbf{x}$. b) We pre-train a CNN based forward model to predict the spectra $\mathbf{tilde{y}}$ associated with a generated design and use it for performance evaluation. The forward model allows for estimating the mean absolute error (MAE) between the spectra of the generated design and the original spectra, providing a quantitative measure of their similarity. In addition, we evaluate the image based MAE of the predicted design as well.
• Figure 2: The general architecture of the conidtional GAN model consists of critic network and generator network. The critic network is used by the Wasserstein GAN training algorithm in the optimization process. During the optimization process, the generator network is trained to generate images that replicate the probability distribution of the training data. Both networks takes conditional label data as input. The label data is the absorption and scattering cross section spectral data of the corresponding training images used to train the model. Proposed in this work is to introduce the conditional label data using label projection in the critic network. The label vector is projected onto the feature vector of the image processing network (blue) with an inner product and this is called label projection. Furthermore we also propose the use of a label embedding network to encode the label data. The label embedding network uses several layers of the one-dimensional convolutions.
• Figure 3: The results in this figure are obtained from the FCGAN-model with and without using label projection and an embedding network in the critic. Figure a) show the original image and figures b) and c) shows the images predicted by the models. Figures d) and e) show the scattering and absorption cross section spectras corresponding to the images. The blue curve is the original data from the finite element simulation of the gold nano structure in the original image. We use a pre-trained convolutional neural network regression model to predict the spectral data for both the original image (dashed red) and the images generated by the model (dashed green and orange). The quality is visibly worse for the image generated from FCGAN compared to when we add label projection and the embedding network. This is also causing a pertubation in the spectral data prediction.
• Figure 4: The models were trained on a dataset containing cylindrical dimer structures and they were evaluated using two different methods. The first method uses a pre-trained convolutional neural network regression model to predict the scattering cross section and absorption cross section spectra. This approach allows us to estimate the MAE between the spectra predicted from real and GAN-generated images. As a second evaluation method, we also estimate the mean absolute error in pixel values between real and generated images. Figures a) and c) shows the results from training the FCGAN architectures figures b) and d) shows the results from training the DCGAN-architecture. We calculate the evaluation metrics by generating n=30 sample images for each labeled original image, and take the average of those when computing the error estimate.
• Figure 5: This figure shows example images from training the FCGAN-models on a larger dataset containing differently shaped anisotropic gold structures. The first row contains the original images, and the other rows contains the corresponding predicted images by the FCGAN-models. The model predictions improve when label projection and the embedding network are added to the model.