Koopman Algorithm for Nonlinear Dynamical System with Uncertainties

The application of big data relies on the profound understanding of the mechanisms behind related fields such as finance and economic fields. However, due to the existence of uncertainty and nonlinearity, this problem faces great challenges, especially for high-dimensional system. A Koopman algorithm is proposed to reconstruct and predict the global behavior of the high-dimensional nonlinear system with uncertainty. Meanwhile, the effectiveness of this Koopman algorithm is verified by taking the three-dimensional Lorenz system as an example. Finally, the future work about the generalization of the Koopman algorithm for high-dimensional nonlinear systems with uncertainty, fractional-order systems, and its applications in financial and economic fields is pointed out.