GRIDS-Net: Inverse shape design and identification of scatterers via geometric regularization and physics-embedded deep learning

TL;DR

This paper introduces GRIDS-Net, a deep learning framework combining geometric regularization and physics-embedded learning to accurately identify and design complex 2D acoustic scatterers, addressing high-dimensional inverse problems.

Contribution

It proposes a novel geometric regularization method using NURBS within a deep neural network for inverse shape design and identification of scatterers.

Findings

Effective prediction of complex 2D scatterer geometries.

Physically consistent acoustic field generation.

Enhanced convergence with physics-embedded learning.

Abstract

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.