Transcranial ultrasound imaging assumes a growing significance in the detection and monitoring of intracranial lesions and cerebral blood flow. Accurate solution of partial differential equation (PDE) is one of the prerequisites for obtaining transcranial ultrasound wavefields. Grid-based numerical solvers such as finite difference (FD) and finite element methods have limitations including high computational costs and discretization errors. Purely data-driven methods have relatively high demands on training datasets. The fact that physics-informed neural network can only target the same model limits its application. In addition, compared to time-domain approaches, frequency-domain solutions offer advantages of reducing computational complexity and enabling stable and accurate inversions. Therefore, we introduce a framework called FD-embedded UNet (FEUNet) for solving frequency-domain transcranial ultrasound wavefields. The PDE error is calculated using the optimal 9-point FD operator, and it is integrated with the data-driven error to jointly guide the network iterations. We showcase the effectiveness of this approach through experiments involving idealized skull and brain models. FEUNet demonstrates versatility in handling various input scenarios and excels in enhancing prediction accuracy, especially with limited datasets and noisy information. Finally, we provide an overview of the advantages, limitations, and potential avenues for future research in this study.
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