Data-Driven Forecasting of Nonlinear System with Herding via Multi-Dimensional Taylor Network

Abstract

This work focuses on developing a forecasting model for the nonlinear system with herding. Firstly, for clear presentation of the mechanism of herding behavior, a concept called intermittent positive feedback is defined. The mathematical expression of intermittent positive feedback is formulated in terms of dead-zone functions with the beginning and ending thresholds in the positive and negative directions. Then a dynamic surrogate based on the intermittent positive feedback multi-dimensional Taylor network is established, and a method for identifying its parameters is proposed. Multi-dimensional Taylor network module simulates the long-term trends of time series. Subsequently, an optimization model based on the alternating iteration of the parameters is developed to enhance the forecast accuracy of the intermittent positive feedback part. Simulation results demonstrate that the forecasting effect of the proposed modeling method is superior to that of conventional non-mechanism data-based surrogates for herding behavior.

Keywords:

• Data-driven modeling of cybernetic systems with herdings
• forecasting
• identification
• intermittent positive feedback
• multi-dimensional Taylor network
• nonlinear time series

Acknowledgments

The authors would like to thank Professor Lu Li for his valuable comments and suggestions.

Disclosure Statement

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work; there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China under grants 61673112 and 60934008, the Fundamental Research Funds for the Central Universities of China under grants 2242017K10003 and 2242014K10031, Shanghai Aerospace Science and Technology Innovation Foundation under grant SAST2019-020, and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).