Multi-step-ahead Prediction from Short-term Data by Delay-embedding-based Forecast Machine

Making accurate multi-step-ahead prediction for a complex system is a challenge for many practical applications, especially when only short-term time-series data are available. In this work, we proposed a novel framework, Delay-Embedding-based Forecast Machine (DEFM), to predict the future values of a target variable in an accurate and multi-step-ahead manner based on the high-dimensional short-term measurements. With a three-module spatiotemporal architecture, DEFM leverages deep learning to effectively extract both the spatially and sequentially associated information from the short-term dynamics even with time-varying parameters or additive noise. Being trained through a self-supervised scheme, DEFM well fits a nonlinear transformation that maps from the observed high-dimensional information to the delay embeddings of a target variable, thus predicting the future information. The effectiveness and accuracy of DEFM is demonstrated by applications on both representative models and six real-world datasets. The comparison with four traditional prediction methods exhibits the superiority and robustness of DEFM.