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

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.