Parallel frequency function-deep neural network for efficient complex broadband signal approximation

TL;DR

This paper introduces PFF-DNN, a neural network approach that leverages Fourier analysis to efficiently fit complex broadband signals with high-frequency components, reducing training time while maintaining accuracy.

Contribution

The paper proposes a novel parallel frequency function-deep neural network (PFF-DNN) that improves fitting efficiency for broadband signals by combining Fourier analysis with spectral bias properties.

Findings

PFF-DNN effectively fits high-frequency broadband signals.

The method reduces computational overhead compared to existing techniques.

Numerical experiments validate the accuracy and efficiency of PFF-DNN.

Abstract

A neural network is essentially a high-dimensional complex mapping model by adjusting network weights for feature fitting. However, the spectral bias in network training leads to unbearable training epochs for fitting the high-frequency components in broadband signals. To improve the fitting efficiency of high-frequency components, the PhaseDNN was proposed recently by combining complex frequency band extraction and frequency shift techniques [Cai et al. SIAM J. SCI. COMPUT. 42, A3285 (2020)]. Our paper is devoted to an alternative candidate for fitting complex signals with high-frequency components. Here, a parallel frequency function-deep neural network (PFF-DNN) is proposed to suppress computational overhead while ensuring fitting accuracy by utilizing fast Fourier analysis of broadband signals and the spectral bias nature of neural networks. The effectiveness and efficiency of the proposed PFF-DNN method are verified based on detailed numerical experiments for six typical broadband signals.