Parallel deep network combining CNN-BiLSTM and Transformer for predicting complex system

Complex systems encounter significant challenges in capturing interaction patterns between global and local information, whose difficulties arise from their nonlinear, multivariable, and high-dimensional characteristics. A network prediction architecture is proposed that integrates an improved Transformer model based on time series reversal and Convolutional Neural Network - Bidirectional Long Short-Term Memory (CNN-BiLSTM) through parallel connection. A sliding window is used to process data. The Inversed Transformer (ITransformer) enhances the global perception of the model and improves the efficiency of capturing inter-variable associations by embedding the complete time series of each variable separately into different channels. The proposed network combines the global information extraction capabilities of the ITransformer with the strengths of CNN-BiLSTM in local temporal modeling. By utilizing gated units for feature fusion, the approach maximizes the use of temporal data, thereby improving prediction performance. Furthermore, the application of the SHapley Additive exPlanations (SHAP) method enhances the transparency of the decision-making process of the model. Finally, numerical simulations demonstrated that the proposed model outperforms existing predictive networks in terms of R<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>, RMSE, and MAE, achieving values of 0.897, 0.148, and 0.119, respectively.