  Advanced radio-frequency pulse design used in magnetic resonance imaging has
recently been demonstrated with deep learning of (convolutional) neural
networks and reinforcement learning. For two-dimensionally selective
radio-frequency pulses, the (convolutional) neural network pulse prediction
time (few milliseconds) was in comparison more than three orders of magnitude
faster than the conventional optimal control computation. The network pulses
were from the supervised training capable of compensating scan-subject
dependent inhomogeneities of B0 and B+1 fields. Unfortunately, the network
presented with a non-negligible percentage of pulse amplitude overshoots in the
test subset, despite the optimal control pulses used in training were fully
constrained. Here, we have extended the convolutional neural network with a
custom-made clipping layer that completely eliminates the risk of pulse
amplitude overshoots, while preserving the ability to compensate the
inhomogeneous field conditions.
