Neural Network Emulator of Spin Ensemble Response to a Sequence of Radio Pulses

The paper proposes a method of developing a neural network emulator of the response of a spin ensemble to a sequence of radio pulses. The emulator was trained using a set containing sequences of RF pulses and responses of the homonuclear spin system calculated by numerical solution of the Bloch equations using the Runge-Kutta method. The deep neural network architecture with recurrent cells is investigated in detail. It is shown that the response of the spin system is adequately represented by two-layer networks with GRU and LSTM cells when the number of cells in a layer is relatively small (less than 64). The best results are obtained for the two-layer architecture in which each of the layers contains 32 GRU cells. To test the generalization ability of the network, its training and validation were performed on different data sets. The training set contained 640 images representing the responses of the spin system to a sequence of two RF pulses with a rectangular envelope. The test set consisted of responses to a sequence of 10 RF pulses. The quality criterion of the prediction was the energy of the difference between the predicted and true responses normalized by the energy of the true response. It is shown that the resulting response prediction error is less than 1%. A full cycle of neural network training on a personal computer of average performance requires no more than 10 min.