A physics-constrained deep learning based approach for acoustic inverse scattering problems

The control of acoustic and elastic waves via engineered materials has several important real world applications such as non-destructive evaluation of structural components, synthesis of biomedical devices, high-resolution imaging, and remote sensing. Being formulated as inverse problems, all these applications share as a common denominator the need for efficient solution methodologies. Available techniques, mostly based on conventional optimization approaches, have shown some significant limitations in terms of the ability to explore a vast design space and to limit the computation burden. In this study, a novel deep auto-encoder (DAE) based approach is proposed in order to solve a benchmark inverse problem consisting in designing assemblies of acoustic scattering elements capable of molding an incoming plane wave into a target (user-defined) downstream pressure distribution. The proposed approach is validated numerically through three design scenarios, involving either a single or multiple scatterer configuration, and target pressure fields defined at different frequencies. The proposed network consists of a geometry estimator and a DAE that imposes constraints due to the physics of the problem on the geometry estimator during the learning process which leads to more robust design. By joint optimization, the estimation of scatterer geometry is strengthened with the latent representations of the target pressure field learned by the DAE. For a trained network, the design inference is quasi-instantaneous given a target 2D pressure field. The generalization capability of the proposed network is further explored by using a dataset generated based on scatterers having new shapes.