System-Informed Neural Network for Frequency Detection

We contrive a deep learning-based frequency analysis scheme called system-informed neural network (SINN) by considering the corresponding linear system model. SINN adopts the adaptive learned iterative soft shrinkage algorithm as the NN architecture and includes the system model in loss function. It has good generalization with fast processing time and finds a solution that satisfies the system model as a physics-informed neural network. To further improve SINN, multiple measurements are exploited by assuming the existence of common frequency components over the measurements. SINN is examined using simulated acoustic data, and the performance is compared to Fourier transform and sparse Bayesian learning (SBL) in terms of the detection/false alarm rate and mean squared error. SINN exhibits clear frequency components in in-situ data tests, as in SBL, by reducing noise effectively. Finally, SINN is applied to noisy passive sonar signals, which include 43 frequency components, and many are recovered.