          Metamaterials are engineered materials that can guide the energy flow with capabilities exceeding those possible in conventional materials, enabling devices by design for the control of acoustic, electromagnetic, and mechanical waves. In this work, we employ supervised as well as unsupervised machine learning techniques to characterize properties of metamaterials that consist of scatterers with cylindrical symmetry along the *z* direction. We build simple models capable of predicting, with reasonable accuracies, the total scattering cross section (TSCS) for certain wavelengths given the configuration of scatterers in two dimensions without any physical knowledge of the problem. The ultimate goal is to be able to solve the inverse problem of predicting configurations given the number of scatteres and desired TSCSs, which would circumvent the computationally expensive optimization problem of finding those configurations.

          We design models based on convolutional neural networks (CNNs) to simulate acoustic multiple scattering from cylindrical structures. CNNs can take advantage of spatial correlations between scatterers giving rise to specific features in the output, here, the TSCS. We test the range of applicability of this model to our problem by considering cases with different numbers of scatterers from 2 to 20, and different wavenumbers of the incoming wave. We train the CNN model using data generated by multiple scattering theory to approximate the TSCS at discrete values of the wavenumber *k~i~a* ∈ \[0.35,045\],(*i* = 1,2...,11), where *a* is the radius of the cylinders. The inputs are binary images of positions of the cylinders, and the output is the 11 values for the TSCS. We consider different CNN architectures and hyperparameters and monitor the training progression in each case using training and validation data sets. Our results show a good correspondence between predicted values and actual TSCS for testing sets that the CNNs have not seen during training. However, we find that the accuracy of training decreases systematically as the number of scatterers increase. We further explore training a deconvolutional neural network in order to solve the inverse problem and construct images given the TSCS.

          In addition, we developed models based on convolutional autoencoder and variational autoencoder architectures. These models take scatterer configuration images as input and, in the process of reproducing the same configurations at the output, can reduce the dimensionality of the data to a small number of latent variables. We train autoencoders whose encoder parts resemble well-performing CNN architectures and examine whether the latent variables have any relationship with the actual TSCS or other physical properties of the system. The decoder part after training with upsampling and deconvolution layers provides a well-conditioned starting point for the design of a deconvolutional neural networks acting as an inverse function that can produce scatterer configurations after further training using TSCS as input for the latent variables.


Convolutional Neural Network Representation of the Total Multiple Scattering Cross Section

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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