Enhancing acoustic scatterer inversion in closed domains with gradient-constrained deep learning

Accurately reconstructing scatterers within closed regions from sparse acoustic measurements presents a challenging inverse problem. Deep learning techniques are widely regarded as effective tools for solving such complex issues. However, conventional approaches often incur significant computational burdens by relying on massive training datasets to boost prediction accuracy. This paper presents an innovative approach that substantially improves network performance not by data augmentation, but by explicitly incorporating physical knowledge through adjoint-derived gradients. The method involves two synergistic stages: firstly, a physics-informed forward model is constructed by integrating gradient information via the adjoint method, which achieves 87 % higher accuracy in acoustic pressure prediction compared to standard data-driven counterparts on the test set; secondly, utilizing the trained forward network as a surrogate model to generate large-scale synthetic datasets for training a robust inverse estimation network. Results demonstrate superior performance: on independent test data, 99.94 % precision in determining scatterer count and high-precision reconstruction with localization resolution of 1/42 wavelength and radius resolution of 1/401 wavelength. Crucially, the method excels even in challenging acoustic shadow zones, surpassing traditional techniques. As the adjoint method is fundamental to sensitivity analysis across computational physics, this gradient-constrained framework can be readily extended to other inverse problems (including inverse electromagnetic scattering and elastic wave-based nondestructive testing) and gradient-based optimization applications like topology optimization, providing a pathway to enhanced accuracy with reduced data dependency.