A deep echo-like spiking neural P systems for time series prediction

The echo-like spiking neural P (ESNP) system is a variant of the echo-state network (ESN) that integrates the nonlinear spiking neural P (NSNP) system. In this study, we propose a deep echo-like spiking neural P system, called the Deep-ESNP model, which extends the ESNP system to better compute the state of the reservoir. Structurally, the Deep-ESNP model can be viewed as a stack of multiple NSNP systems equipped with input and output layers. This deep-stacked reservoir provides powerful nonlinear dynamics for the Deep-ESNP model. Similarly, the weights of the input and stacked NSNP systems are fixed during the initialisation phase, and the output weights are trained using the ridge regression algorithm. The Deep-ESNP model was evaluated on six benchmark time-series datasets and a real-world task of precipitation prediction and further compared with 26 state-of-the-art baseline prediction models. The experimental results show that the Deep-ESNP model has excellent prediction performance, indicating that it is suitable for time-series prediction.