  Purpose: Rapid 2D RF pulse design with subject specific $B_1^+$ inhomogeneity
and $B_0$ off-resonance compensation at 7 T predicted from convolutional neural
networks is presented.
  Methods: The convolution neural network was trained on half a million
single-channel transmit, 2D RF pulses optimized with an optimal control method
using artificial 2D targets, $B_1^+$ and $B_0$ maps. Predicted pulses were
tested in a phantom and in vivo at 7 T with measured $B_1^+$ and $B_0$ maps
from a high-resolution GRE sequence.
  Results: Pulse prediction by the trained convolutional neural network was
done on the fly during the MR session in approximately 9 ms for multiple hand
drawn ROIs and the measured $B_1^+$ and $B_0$ maps. Compensation of $B_1^+$
inhomogeneity and $B_0$ off-resonances has been confirmed in the phantom and in
vivo experiments. The reconstructed image data agrees well with the simulations
using the acquired $B_1^+$ and $B_0$ maps and the 2D RF pulse predicted by the
convolutional neural networks is as good as the conventional RF pulse obtained
by optimal control.
  Conclusion: The proposed convolutional neural network based 2D RF pulse
design method predicts 2D RF pulses with an excellent excitation pattern and
compensated $B_1^+$ and $B_0$ variations at 7 T. The rapid 2D RF pulse
prediction (9 ms) enables subject-specific high-quality 2D RF pulses without
the need to run lengthy optimizations.
