A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound

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 online during treatments predict acoustic field passing through skull (e.g., account subject-specific dose and targeting variations). As a step towards real-time predictions, in current work, fast iterative solver heterogeneous Helmholtz equation 2D developed using fully-learned optimizer. The lightweight network architecture based on modified UNet that includes learned hidden state. trained physics-based loss function set idealized sound speed distributions with fully unsupervised training (no knowledge true solution required). optimizer shows excellent performance test set, capable generalization well outside examples, including much larger computational domains, more complex source distributions, example, those derived from x-ray computed tomography images skull.