A novel framework for direct multistep prediction in complex systems

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.

Automated summary

Multistep prediction has long been a challenge in many real-world systems. This paper proposes a combination framework called Spatial-Temporal Mapping (STM), which uses Gaussian process regression and delay embedding to address the shortcomings of previous approaches. Experimental results demonstrate that STM outperforms traditional iterative methods in various model and real-world systems, and has potential applications in other practical systems.