Causal-Transformer: Spatial-temporal causal attention-based transformer for time series prediction

Real-time monitoring and accurate prediction of key variables are indispensable to ensure industrial production activities proceed as expected. With the increase in measurement data volume and the improvement of hardware computing power, the Transformer and its variants, due to their excellent capability in extracting global dependencies, are playing an increasingly important role among deep learning-based multidimensional time series prediction models. In addition, from the perspective of causality, cause variables contain parts of information in effect variables and can reduce the uncertainty of effect variables, which is beneficial for prediction. However, there has been relatively limited research on combining the Transformer and causal feature analysis. To fully use both advantages, this paper introduces the Causal-Transformer (CT) model, which utilizes semi-orthogonal projection to extract causal features from multiple input variables. A multi-head spatial-temporal causal attention mechanism is designed in the encoder block based on the classical Transformer model to simultaneously reduce feature dimensions and extract implicit causal features in both the temporal and spatial dimensions. The CT also utilizes the Granger causality analysis to select the causal teaching indicators of target variables to provide stable assistance by injecting explicit causality into the inputs of the decoder block. By leveraging more condensed and independent causal features, the CT possesses inherent advantages in predicting time series variables. Case study results show that the CT model outperforms the other models on the diesel refinery dataset, especially with a reduction of 46.0% and 30.4% in MSE towards the classic Transformer and informer in five-step prediction.