Publications

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Multiple scattering is a common phenomenon in acoustic media that arises from the interaction of the acoustic field with a network of scatterers. This mechanism is dominant in problems such as the design and simulation of acoustic metamaterial structures often used to achieve acoustic control for sound isolation, and remote sensing. In this study, we present a physics-informed neural network (PINN) capable of simulating the propagation of acoustic waves in an infinite domain in the presence of multiple rigid scatterers. This approach integrates a deep neural network architecture with the mathematical description of the physical problem in order to obtain predictions of the acoustic field that are consistent with both governing equations and boundary conditions. The predictions from the PINN are compared with those from a commercial finite element software model in order to assess the performance of the method.

This study presents a deep learning based methodology for both remote sensing and design of acoustic scatterers. The ability to determine the shape of a scatterer, either in the context of material design or sensing, plays a critical role in many practical engineering problems. This class of inverse problems is extremely challenging due to their high-dimensional, nonlinear, and ill-posed nature. To overcome these technical hurdles, we introduce a geometric regularization approach for deep neural networks (DNN) based on non-uniform rational B-splines (NURBS) and capable of predicting complex 2D scatterer geometries in a parsimonious dimensional representation. Then, this geometric regularization is combined with physics-embedded learning and integrated within a robust convolutional autoencoder (CAE) architecture to accurately predict the shape of 2D scatterers in the context of identification and inverse design problems. An extensive numerical study is presented in order to showcase the remarkable ability of this approach to handle complex scatterer geometries while generating physically-consistent acoustic fields. The study also assesses and contrasts the role played by the (weakly) embedded physics in the convergence of the DNN predictions to a physically consistent inverse design.

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In this study, we develop an end-to-end deep learning-based inverse design approach to determine the scatterer shape necessary to achieve a target acoustic field. This approach integrates non-uniform rational B-spline (NURBS) into a convolutional autoencoder (CAE) architecture while concurrently leveraging (in a weak sense) the governing physics of the acoustic problem. By utilizing prior physical knowledge and NURBS parameterization to regularize the ill-posed inverse problem, this method does not require enforcing any geometric constraint on the inverse design space, hence allowing the determination of scatterers with potentially any arbitrary shape (within the set allowed by NURBS). A numerical study is presented to showcase the ability of this approach to identify physically-consistent scatterer shapes capable of producing user-defined acoustic fields.

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