  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.
