Physics-Informed Deep Learning for 2-D Phased Array Beamforming With Imperfection Tolerance

Designing efficient and reliable two-dimensional (2D) beamforming for phased array antennas (PAAs) remains a significant challenge because of the heavy computational demands involved. In this study, we introduce a beamforming framework that adopts a physics-informed deep neural network (PIDNN). The proposed model incorporates physical principles directly into the training process through a customized loss function, which minimizes the mean squared error between the array response and a target reference signal. The beamforming weights produced by the PIDNN are systematically evaluated against the theoretically optimal Wiener solution. To assess robustness, the method is implemented on an 8×8 PAA and evaluated against both a shallow architecture—the radial basis function neural network (RBFNN)—and a deeper model, the convolutional neural network (CNN). Moreover, the PIDNN is applied to a large PAA to assess its performance when the number of antenna elements increases. Experimental results demonstrate that the PIDNN closely approximates Wiener-optimal weights while maintaining robustness to array imperfections and achieving this with markedly reduced computational cost.