An Integrated Reservoir Predictor Based on Spatiotemporal Information Transformation

Abstract

Multistep prediction of high-dimensional time series is an essential and challenging task. In this study, we propose an integrated reservoir predictor for making accurate and robust multistep-ahead forecasts based on short-term high-dimensional time series. Initially, a conjugated pair of Spatiotemporal Information (STI) equations is derived using Takens’ embedding theory to transform the spatial information of high-dimensional variables into one-dimensional temporal information of the target variable and vice versa. Next, by exploiting reservoir networks, reservoir-based STI equations are established to efficiently capture nonlinear dynamics of the target system with only linear optimization. Then, through an integration phase, the integrated reservoir predictor can output precise and robust predictions of the multistep-ahead states of any target variable. The integrated reservoir predictor outperforms some other prediction methods (including reservoir computing, long-short-term-memory network, convolutional neural network and support vector regression), when applied to classical dynamic systems (e.g. 60D double scroll model, 40D Lorenz 96 model, and 60D Rössler model) and real-world datasets (solar generation data and PM2.5 concentration records), as indicated by evaluation metrics such as Pearson correlation coefficients exceeding 0.9 and root-mean-square errors below 0.3, even in the presence of noise in training data.