Butterfly-Net2: Simplified Butterfly-Net and Fourier Transform Initialization
This work addresses efficiency improvements in CNNs for PDEs and signal processing, though it appears incremental by simplifying an existing architecture and adding a new initialization.
The paper introduces BNet2, a simplified structured CNN, and a Fourier transform initialization method, achieving similar accuracy as conventional CNNs with fewer parameters and improved training/testing accuracy across tasks like PDE solving and signal denoising.
Structured CNN designed using the prior information of problems potentially improves efficiency over conventional CNNs in various tasks in solving PDEs and inverse problems in signal processing. This paper introduces BNet2, a simplified Butterfly-Net and inline with the conventional CNN. Moreover, a Fourier transform initialization is proposed for both BNet2 and CNN with guaranteed approximation power to represent the Fourier transform operator. Experimentally, BNet2 and the Fourier transform initialization strategy are tested on various tasks, including approximating Fourier transform operator, end-to-end solvers of linear and nonlinear PDEs, and denoising and deblurring of 1D signals. On all tasks, under the same initialization, BNet2 achieves similar accuracy as CNN but has fewer parameters. And Fourier transform initialized BNet2 and CNN consistently improve the training and testing accuracy over the randomly initialized CNN.