DEFM: Delay E mbedding based Forecast Machine for Time Series Forecasting by Spatiotemporal Information Transformation

TL;DR

DEFM is a novel deep learning framework that uses delay embedding theory to transform high-dimensional spatiotemporal data into a form suitable for accurate multistep forecasting, demonstrating superior performance on chaotic systems and real-world datasets.

Contribution

This work introduces DEFM, combining delay embedding theory with deep neural networks for improved multistep time series forecasting of complex spatiotemporal systems.

Findings

DEFM outperforms five existing prediction methods in accuracy and robustness.

DEFM effectively captures spatiotemporal dynamics in chaotic systems.

DEFM demonstrates strong generalization on diverse real-world datasets.

Abstract

Making accurate forecasts for a complex system is a challenge in various practical applications. The major difficulty in solving such a problem concerns nonlinear spatiotemporal dynamics with time-varying characteristics. Takens' delay embedding theory provides a way to transform high-dimensional spatial information into temporal information. In this work, by combining delay embedding theory and deep learning techniques, we propose a novel framework, Delay-Embedding-based Forecast Machine (DEFM), to predict the future values of a target variable in a self-supervised and multistep-ahead manner based on high-dimensional observations. With a three-module spatiotemporal architecture, the DEFM leverages deep neural networks to effectively extract both the spatially and temporally associated information from the observed time series even with time-varying parameters or additive noise. The DEFM can accurately predict future information by transforming spatiotemporal information to the delay embeddings of a target variable. The efficacy and precision of the DEFM are substantiated through applications in three spatiotemporally chaotic systems: a 90-dimensional (90D) coupled Lorenz system, the Lorenz 96 system, and the Kuramoto-Sivashinsky (KS) equation with inhomogeneity. Additionally, the performance of the DEFM is evaluated on six real-world datasets spanning various fields. Comparative experiments with five prediction methods illustrate the superiority and robustness of the DEFM and show the great potential of the DEFM in temporal information mining and forecasting