Transcranial ultrasound therapy is increasingly used for the non-invasive treatment of brain disorders. However, conventional numerical wave solvers are currently too computationally expensive to be used online during treatments to predict the acoustic field passing through the skull (e.g., to account for subject-specific dose and targeting variations). As a step towards real-time predictions, in the current work, a fast iterative solver for the heterogeneous Helmholtz equation in 2D is developed using a fully-learned optimizer. The lightweight network architecture is based on a modified UNet that includes a learned hidden state. The network is trained using a physics-based loss function and a set of idealized sound speed distributions with fully unsupervised training (no knowledge of the true solution is required). The learned optimizer shows excellent performance on the test set, and is capable of generalization well outside the training examples, including to much larger computational domains, and more complex source and sound speed distributions, for example, those derived from x-ray computed tomography images of the skull.

经颅超声治疗越来越多地用于脑部疾病的非侵入性治疗。然而，传统的数值波求解器目前的计算成本太高，无法在治疗期间在线使用以预测穿过头骨的声场（例如，考虑受试者特定的剂量和靶向变化）。作为迈向实时预测的一步，在当前的工作中，使用完全学习的优化器开发了二维异构亥姆霍兹方程的快速迭代求解器。轻量级网络架构基于修改后的 UNet，其中包括学习的隐藏状态。该网络使用基于物理的损失函数和一组理想化的声速分布进行训练，并进行完全无监督的训练（不需要了解真正的解决方案）。