论文标题
使用无监督学习的Helmholtz方程求解器：应用于经颅超声
A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound
论文作者
论文摘要
经颅超声疗法越来越多地用于脑疾病的非侵入性治疗。但是，常规的数值波求解器当前在计算上太昂贵，无法在治疗过程中在线使用，以预测通过头骨的声场（例如，以特定于主题的剂量和靶向变化）。作为迈向实时预测的一步，在当前工作中，使用完全学习的优化器开发了2D中异质Helmholtz方程的快速迭代求解器。轻型网络体系结构基于一个修改后的UNET，其中包括一个学习的隐藏状态。使用基于物理的损失功能和一组理想化的音速分布对网络进行训练，并具有完全无监督的培训（不需要对真实解决方案的了解）。学到的优化器在测试集上显示出卓越的性能，并且能够在训练示例之外进行概括（包括更大的计算域），以及更复杂的源和声速分布，例如，这些分布来自X射线计算机的颅骨图像。
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.
