Deep Recurrent Stochastic Configuration Networks for Modelling Nonlinear Dynamic Systems

Deep learning techniques have shown promise in various domains. However, traditional methods can only demonstrate their universal approximation capability from an existential perspective, failing to explicitly construct such networks. This limitation is pronounced in nonlinear dynamic modelling, especially when faced with continual changes and uncertainties in the process, making them struggle to achieve accurate predictions and responses. This paper proposes a novel deep reservoir computing framework, termed deep recurrent stochastic configuration network (DeepRSCN) for problem solving. DeepRSCNs are incrementally constructed, with all reservoir nodes directly linked to the final output. The input random weight matrix and a special structure of the random reservoir weight matrix are assigned in the light of a supervisory mechanism, ensuring the universal approximation property. The output weights are updated online using the projection algorithm to handle the unknown dynamics. Given a set of training samples, DeepRSCNs can quickly generate learning representations, which consist of random basis functions with cascaded input and readout weights. Experimental results over a time series prediction, a nonlinear system identification problem, and an industrial data predictive analysis demonstrate that the proposed DeepRSCN outperforms other state-of-the-art methods with sound learning and generalization performance.