We propose a method to design acoustic metamaterial configurations using deep learning and generative modeling targeting low total scattering cross section (TSCS) responses. We combine a conditional Wasserstein Generative Adversarial Network (cWGAN) with a standard Convolutional Neural Network (CNN) to generate metacluster configurations with a specified TSCS. Using our proprietary multiple scattering solver with MATLAB optimization toolbox, we generate a dataset with random configurations of 2 and 4 rigid cylinder scatterers. We use the optical theorem to formulate the TSCS in terms of the forward scattering amplitude, with an incident plane wave propagating in the positive x direction, and we evaluate the TSCS within a discrete range of wavenumbers. This dataset is composed of 60,000 64x64 pixel resolution images and their corresponding TSCS as an 11-unit vector between the wavenumber range 0.35 and 0.45 inclusively. Additionally, we use MATLAB’s fmincon algorithm to generate a dataset of optimized 2-scatterer and 4-scatterer configurations.A few components are necessary to achieve a deep learning model capable of inversely designing scatterer configurations: a generative model capable of producing realistic designs, a method to enable the model to generate images with specified responses, and an evaluator that can confirm the validity of generated images. To develop our cWGAN model1­, we first select the standard GAN as our generative model. &nbsp;A conditional feature is applied to the GAN to allow the generative model to produce images of configurations given specified design parameters. We train the GAN to correlate scatterer configuration images with the corresponding TSCS. Additionally, we incorporate the Wasserstein distance as the objective function to reduce mode collapse and the novel CoordConv layer to assist the model in generating more accurate images. We develop and train a CNN model that receives scatterer configuration images and approximates the TSCS across a discrete wavenumber range. We use the random configuration dataset and reserve 10,000 samples as the test set. We partition the remaining datapoints for an 80% train and 20% validation split. This CNN model examines the proposed images by the generator and returns the approximated TSCS.We use the random configuration dataset initially to train the cWGAN; images of 2-scatter and 4-scatterer configurations along with the corresponding TSCS as labels are passed into the generator. The WGAN critic evaluates the Wasserstein distance between real images and generated images, while the CNN model evaluates the TSCS of generated images. Both the Wasserstein loss from the critic and the mean squared error loss from the CNN model contribute to the generator’s learning process. We partition the random configuration training set into an 80% train and 20% test split, where the test set will be used to validate the TSCS of generated configurations. Upon training completion, the generator is capable of producing various scatterer designs given specified TSCS.Extending this model to optimized scatterer configurations, we continue to train the cWGAN using the optimal scatterer position dataset with minimal TSCS as labels. Following the training, we allow the generator to produce scatterer configuration images with minimized TSCS. We validate the generated images using our MS solver and compare the TSCS response of the generated configurations with the expected TSCS. Results show that the generator has found scatterer configurations with TSCS responses that are comparable or even better than the expected TSCS.References[1]. Peter Lai, Feruza Amirkulova, and Peter Gerstoft. Conditional Wasserstein Generative Adversarial Networks Applied to Acoustic Metamaterial Design (submitted to JASA, under review).

Acoustic Metamaterial Design Using Conditional Wasserstein Generative Adversarial Networks

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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