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.

翻译：以鲁棒方式进行预测是一项困难的任务，尤其当仅基于非线性系统的观测数据时。本研究开发了一种神经网络计算框架——时空信息转换机，通过采用时空信息转换，高效且准确地实现时间序列的多步超前预测。STICM结合了时空信息方程与时序卷积网络的优势，将高维/空间数据映射到目标变量的未来时间值，从而自然地提供目标变量的预测。基于观测变量，STICM还在格兰杰因果意义上推断目标变量的因果因素，这些因素被选为有效的空间信息以提升时间序列预测的鲁棒性。STICM已成功应用于基准系统和真实世界数据集，结果表明其在多步超前预测中表现出优越且鲁棒的性能，即使数据受到噪声干扰。从理论和计算两个角度来看，STICM在人工智能实际应用中具有巨大潜力，或可作为仅基于观测数据的无模型方法，同时为机器学习领域以动态方式探索观测高维数据开辟了新途径。