  Making predictions 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 multistep-ahead prediction 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
prediction 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 prediction robustness of time-series. The STICM was successfully
applied to both benchmark systems and real-world datasets, all of which show
superior and robust performance in multistep-ahead prediction, 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 (AI) 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.
