A Bayesian optimization framework for two-dimensional sparse array design driven by physics-based simulation

Traditional design of underwater two-dimensional arrays focuses on local beam-pattern metrics, with insufficient attention paid to the overall imaging performance in practical acoustic environments. To mitigate this limitation, this paper proposes a collaborative array design framework that integrates physical acoustic simulation with Bayesian optimization. Employing a Gaussian process as the surrogate model, the framework incorporates a dual-stage delay optimization strategy and a composite loss function to enable the automatic search for optimal array configurations. Simulation experiment results demonstrate that within a 90° × 90° field of view, the proposed DSDO method reduces the maximum delay mean square error by approximately 66.7% compared with the Fresnel approximation. The segmentation performance metrics (peak signal-to-noise ratio, structural similarity, intersection over union, and accuracy) of the images obtained by the optimized array show improvements of 6.49%, 1.62%, 6.21%, and 2.17%, respectively, compared to the Fermat spiral array. This indicates that the method enhances the clarity and structural fidelity of targets within the images, laying a foundation for subsequent downstream tasks, such as target detection and recognition.