Extended Kalman filter-based Elman networks for industrial time series prediction with GPU acceleration

Accurately and rapidly predicting a time series is a hot research issue in the current applied sciences field. Compared to gradient-based methods, the existing extended Kalman filter (EKF)-based recurrent neural network (RNN) improved the convergence rate of training, but its computing for the Jacobian matrix was usually complicated and time-consuming. In this study, considering the structural feature of the Elman network and the modeling demand in industrial application, a new direct calculation of the Jacobian matrix for Elman networks is proposed and the corresponding matrix solution is clearly derived, which greatly simplifies the solving process and helps to realize its parallelization. Given the industrial real-time demand, a parallelized method is then reported to model the Elman network, which shifts the computational intensive tasks of network training on graphics processing unit (GPU) for the modeling efficiency. To demonstrate the performance of the proposed method, a number of experimental instances are presented, including the Mackey–Glass time series with additive Gaussian white noise and a real-world industrial application—byproduct gas flow prediction in the steel industry. The results indicate that the proposed method exhibits the merits of rapid modeling, strong generalization and good stability.