  Multivariate time series (MTS) forecasting has been extensively applied
across diverse domains, such as weather prediction and energy consumption.
However, current studies still rely on the vanilla point-wise self-attention
mechanism to capture cross-variable dependencies, which is inadequate in
extracting the intricate cross-correlation implied between variables. To fill
this gap, we propose Variable Correlation Transformer (VCformer), which
utilizes Variable Correlation Attention (VCA) module to mine the correlations
among variables. Specifically, based on the stochastic process theory, VCA
calculates and integrates the cross-correlation scores corresponding to
different lags between queries and keys, thereby enhancing its ability to
uncover multivariate relationships. Additionally, inspired by Koopman dynamics
theory, we also develop Koopman Temporal Detector (KTD) to better address the
non-stationarity in time series. The two key components enable VCformer to
extract both multivariate correlations and temporal dependencies. Our extensive
experiments on eight real-world datasets demonstrate the effectiveness of
VCformer, achieving top-tier performance compared to other state-of-the-art
baseline models. Code is available at this repository:
https://github.com/CSyyn/VCformer.
