Predicting future dynamics from short-term time series using an Anticipated Learning Machine

Abstract

Abstract Predicting time series has significant practical applications over different disciplines. Here, we propose an Anticipated Learning Machine (ALM) to achieve precise future-state predictions based on short-term but high-dimensional data. From non-linear dynamical systems theory, we show that ALM can transform recent correlation/spatial information of high-dimensional variables into future dynamical/temporal information of any target variable, thereby overcoming the small-sample problem and achieving multistep-ahead predictions. Since the training samples generated from high-dimensional data also include information of the unknown future values of the target variable, it is called anticipated learning. Extensive experiments on real-world data demonstrate significantly superior performances of ALM over all of the existing 12 methods. In contrast to traditional statistics-based machine learning, ALM is based on non-linear dynamics, thus opening a new way for dynamics-based machine learning.