A recursive digital filter as a unit of a recurrent neural network in the problem of predicting the response of a spin system

Predicting the response of a physical system to a control action based on the results of observing its dynamics is one of the urgent tasks of machine learning. It is often difficult to monitor the dynamics of the system during the control action. Then a model is required, which can be trained with a partially hidden response. The paper considers predicting the reaction of a spin ensemble to a sequence of radio frequency pulses using artificial neural networks. Several network architectures with different standard recurrent units have been compared: GRU, LSTM, and SCRN. It is shown that networks with the listed units are poorly trainable if there is an additional time delay between the response and the impact. The paper also proposes and investigates a compact and noise-tolerant recurrent cell similar to a digital recursive filter with infinite impulse response. The error in predicting the response of a neural network based on it does not exceed 11% with a signal-to-noise ratio of 0 dB. This cell differs from the standard ones in that its output signal is calculated using several previous states. Such a simple modification significantly reduced the duration of model training, even in the case of partially hidden dynamics of the physical system.