An encoder–decoder architecture with Fourier attention for chaotic time series multi-step prediction

Abstract

Multi-step prediction of chaotic time series has been a challenging problem. An encoder–decoder architecture based on novel Fourier attention was proposed, called FGNet, applied to chaotic time series multi-step prediction. Two perspectives were carefully re-considered in modeling, one was the integrated use of frequency and temporal domain information, the other was the fusion of channel information and series information. The encoder was a self-attention architecture with Fourier attention module for capturing dynamic information in time series. Correspondingly, the decoder used the Gated Recurrent Unit (GRU) module with identity mapping, and the decoder was used to model the representation based on temporal dependency. For the interpretability deficiency of Fourier attention in FNet, which was proposed by google, a novel Fourier attention module was proposed. Specifically, the frequency domain features were extracted using Fourier transform, series and channel features were integrated capture through channel swapping coupling. Then these features were fused in the frequency domain space to enhance feature representation and their interpretability is achieved through inverse Fourier transform. Simulated data (Mackey–Glass system and Lorenz) and real data (sunspot time series) were used to verify that FGNet proposed achieves pleasantly surprising multi-step prediction performance in practice.