Deep operator network for periodic signal problem with application to central blood pressure monitoring

Abstract

Periodic signals are commonly used in communication and control systems, such as bio-signal, sound signal and AC current signal. One of periodic signals, central blood pressure has an essential role for preventing cardiovascular diseases which is the world leading cause of deaths. Higher central blood pressure can lead to heart failure, aneurysms and strokes, therefore, we need to monitor central blood pressure waveform carefully to prevent cardiovascular diseases. However, the number of blood pressure data acquired through clinical experiments is few, which leads to poor network performance. That’s why Few-Shot Learning for central blood pressure monitoring is required. The Deep Operator Network is appropriate for learning these few periodic signals since it is able to learn non-linear operators. In this study, Deep Operator Network learns frequency as an uncertain variable at the trunknet. Cycle normalization method, which slices the signal with multi cycles into a cycle, is proposed to prevent that the multi cycles of periodic signals result in large errors. Period normalization methods, which normalizes the time input by a period, are proposed for Deep Operator Network to learn time inputs equally at the trunknet. The proposed Deep Operator Network is validated with the simulated periodic data using a transfer function. Also, it is applied to the blood pressure data from a non-linear system. Three proposed methods are all necessary for the Deep Operator Network to succeed learning periodic signal from non-linear system. Training a frequency in the trunknet helps the model express untrained frequencies, and the cycle normalization allows the model to work efficiently with a single cycle. Lastly period normalization prevents the imbalanced learning over time. As a result, the SBP, DBP, and Augmentation Index (AIx) of the predicted waveform has an error of $-0.78\pm 1.36 mmHg$, $-0.40\pm 1.44 mmHg$, and $-0.85\pm 1.84 %$ respectively.