DEFM: Delay-embedding-based forecast machine for time series forecasting by spatiotemporal information...

Area of Science:

• Complex Systems Science
• Data Science
• Applied Mathematics

Background:

• Forecasting complex systems is challenging due to nonlinear spatiotemporal dynamics and time-varying characteristics.
• Takens' delay embedding theory offers a method to convert high-dimensional spatial data into temporal information.

Purpose of the Study:

• To propose a novel framework, the delay-embedding-based forecast Machine (DEFM), for accurate, self-supervised, multistep-ahead forecasting.
• To leverage deep learning and delay embedding theory to handle complex spatiotemporal dynamics.

Main Methods:

• Development of the DEFM, a three-module spatiotemporal deep learning architecture.
• Integration of Takens' delay embedding theory with deep neural networks to extract spatiotemporal information.
• Application of the framework to chaotic systems and real-world datasets.

Main Results:

• The DEFM accurately predicts future values by transforming spatiotemporal information into delay embeddings.
• Demonstrated efficacy and precision on chaotic systems (90D Lorenz, Lorenz 96, Kuramoto-Sivashinsky) and six real-world datasets.
• Comparative experiments show the DEFM's superiority and robustness over five other prediction methods.

Conclusions:

• The DEFM framework exhibits significant potential for temporal information mining and forecasting in complex systems.
• The method effectively addresses challenges posed by time-varying parameters and additive noise in spatiotemporal data.
• DEFM provides a robust and accurate approach for multistep-ahead prediction in diverse applications.