Modeling a Multi-Element Ultrasound Transducer via Component-Focused Physics-informed Neural Networks

The accurate modeling of wavefields is a crucial aspect of ultrasound therapeutics. Physics-Informed Neural Networks (PINNs) are recognized as potent tools for solving Partial Differential Equations (PDEs) in ultrasound modeling. However, similar to other deep learning methods, PINNs face challenges in training, and the oscillatory nature of the Linear Wave Equation (LWE) adds to their complexity. Additionally, the presence of a forcing time-dependent source term in the LWE necessitates careful consideration when training PINNs to avoid erroneous predictions. This study aims to enhance the accuracy and convergence of ultrasound wavefield modeling, specifically for a multielement focused ultrasound transducer (FUST), through an innovative component-focused PINN architecture. This architecture integrates both Convolutional Neural Networks (CNN) and Feed-forward Neural Networks (FNN) as approximator networks. Our approach separates attention from the different terms of LWE. By employing a combination of CNN and FNN within the PINN architecture, the model focuses separately on the components of the LWE. This approach does not require previously known solutions as the training data. When using the Finite Difference Time Domain (FDTD) method as the true solution, the proposed component-focused PINN architecture demonstrates a significant reduction in L2 relative error (L2RE) compared to PINN models using standard fully-connected FNNs. Additionally, our model exhibits faster convergence, which contributes to increased efficiency in ultrasound wavefield modeling. This innovative approach has potential implications for the advancement of modeling using deep-learning methods in ultrasound therapeutics.