通过解耦幅相关系提升多变量时序预测的平稳性建模能力
Stationarity Exploration for Multivariate Time Series Forecasting
- 提出幅相重构网络，显式建模幅度与相位的相互关系
- 在多个数据集上超越现有最优方法，显著提升平稳特征捕捉能力
- 适合需要精准建模周期与动态变化的时序预测任务
基于深度学习的时间序列预测已广泛应用。近年来，将时间序列转换到频域以准确挖掘周期模式变得流行，但现有方法难以有效提取复杂交织频段中的平稳信息。本文提出一种简单而有效的幅度-相位重构网络（APRNet），通过建模幅度与相位之间的相互关系，避免二者受不同物理量约束，从而解耦信号的独立特征以捕捉平稳性。具体地，该模型在序列与通道维度上表示多变量时间序列输入，突出多交互频率下幅度与相位的相关性；提出基于柯尔莫哥洛夫-阿诺德网络的局部相关性（KLC）模块，利用一维函数自适应拟合局部函数，更灵活刻画不同幅度与相位下的平稳特征，显著增强对时变模式的建模能力。大量实验表明，APRNet在多个基准数据集上优于当前最先进方法。
原文摘要 · Abstract (English)
Deep learning-based time series forecasting has found widespread applications. Recently, converting time series data into the frequency domain for forecasting has become popular for accurately exploring periodic patterns. However, existing methods often cannot effectively explore stationary information from complex intertwined frequency components. In this paper, we propose a simple yet effective Amplitude-Phase Reconstruct Network (APRNet) that models the inter-relationships of amplitude and phase, which prevents the amplitude and phase from being constrained by different physical quantities, thereby decoupling the distinct characteristics of signals for capturing stationary information. Specifically, we represent the multivariate time series input across sequence and channel dimensions, highlighting the correlation between amplitude and phase at multiple interaction frequencies. We propose a novel Kolmogorov-Arnold-Network-based Local Correlation (KLC) module to adaptively fit local functions using univariate functions, enabling more flexible characterization of stationary features across different amplitudes and phases. This significantly enhances the model's capability to capture time-varying patterns. Extensive experiments demonstrate the superiority of our APRNet against the state-of-the-arts (SOTAs).
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