Spatiotemporal information conversion machine for time-series forecasting.

Making time-series forecasting in a robust way is a difficult task only based on the observed data of a nonlinear system. In this work, a neural network computing framework, the spatiotemporal information conversion machine (STICM), was developed to efficiently and accurately render a forecasting of a time series by employing a spatial-temporal information (STI) transformation. STICM combines the advantages of both the STI equation and the temporal convolutional network, which maps the high-dimensional/spatial data to the future temporal values of a target variable, thus naturally providing the forecasting of the target variable. From the observed variables, the STICM also infers the causal factors of the target variable in the sense of Granger causality, which are in turn selected as effective spatial information to improve the robustness of time-series forecasting. The STICM was successfully applied to both benchmark systems and real-world datasets, all of which show superior and robust performance in time-series forecasting, even when the data were perturbed by noise. From both theoretical and computational viewpoints, the STICM has great potential in practical applications in artificial intelligence or as a model-free method based only on the observed data, and also opens a new way to explore the observed high-dimensional data in a dynamical manner for machine learning.