Considering true values cannot be available at every time step in an online learning algorithm for multi-step-ahead (MSA) forecasts, a MSA reinforced real-time recurrent learning algorithm for recurrent neural networks (R-RTRL NN) is proposed. The main merit of the proposed method is to repeatedly adjust model parameters with the current information including the latest observed values and model’s outputs to enhance the reliability and the forecast accuracy of the proposed method. The sequential formulation of the R-RTRL NN is derived. To demonstrate its reliability and effectiveness, the proposed R-RTRL NN is implemented to make 2-, 4- and 6-step-ahead forecasts in a famous benchmark chaotic time series and a reservoir flood inflow series in North Taiwan. For comparison purpose, three comparative neural networks (two dynamic and one static neural networks) were performed. Numerical and experimental results indicate that the R-RTRL NN not only achieves superior performance to comparative networks but significantly improves the precision of MSA forecasts for both chaotic time series and reservoir inflow case during typhoon events with effective mitigation in the time-lag problem.
