Graphformer: Adaptive graph correlation transformer for multivariate long sequence time series forecasting

Accurate long sequence time series forecasting (LSTF) remains a key challenge due to its complex time-dependent nature. Multivariate time series forecasting methods inherently assume that variables are interrelated and that the future state of each variable depends not only on its history but also on other variables. However, most existing methods, such as Transformer, cannot effectively exploit the potential spatial correlation between variables. To cope with the above problems, we propose a Transformer-based LSTF model, called Graphformer, which can efficiently learn complex temporal patterns and dependencies between multiple variables. First, in the encoder's self-attentive downsampling layer, Graphformer replaces the standard convolutional layer with an dilated convolutional layer to efficiently capture long-term dependencies between time series at different granularity levels. Meanwhile, Graphformer replaces the self-attention mechanism with a graph self-attention mechanism that can automatically infer the implicit sparse graph structure from the data, showing better generality for time series without explicit graph structure and learning implicit spatial dependencies between sequences. In addition, Graphformer uses a temporal inertia module to enhance the sensitivity of future time steps to recent inputs, and a multi-scale feature fusion operation to extract temporal correlations at different granularity levels by slicing and fusing feature maps to improve model accuracy and efficiency. Our proposed Graphformer can improve the long sequence time series forecasting accuracy significantly when compared with that of SOTA Transformer-based models.