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Journal Article

A novel framework for direct multistep prediction in complex systems


Wu,  Tao
Potsdam Institute for Climate Impact Research;

An,  Feng
External Organizations;

Gao,  Xiangyun
External Organizations;

Zhong,  Weiqiong
External Organizations;


Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

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Wu, T., An, F., Gao, X., Zhong, W., Kurths, J. (2023): A novel framework for direct multistep prediction in complex systems. - Nonlinear Dynamics, 111, 9289-9304.

Cite as: https://publications.pik-potsdam.de/pubman/item/item_28294
Multistep prediction is an open challenge in many real-world systems for a long time. Despite the advantages of previous approaches, e.g., step-by-step iteration, they have some shortcomings, such as accumulated errors, high cost, and low interpretation. To this end, Gaussian process regression and delay embedding are used to create a combination framework, namely spatial–temporal mapping (STM). Delay embedding is employed to reconstruct an isomorphic dynamical structure with the original system through a single time series, which provides the fundamental architecture for multistep predictions (interpretation). Gaussian process regression is used to achieve predictions by identifying a mapping between the reconstructed dynamical structure and the original structure. This combination framework outputs multistep ahead predictions in a single step (low cost). We test the feasibility of STM for both model systems, including the 3-species ecology system, the Lorenz chaotic system, and the Rossler chaotic system, and several real-world systems, involving energy, finance, life science, and climate. STM framework outperforms traditional iterative approaches and has the potential for many other real-world systems.