The optimal truncated low-dimensional dynamical systems based on flow databases

A new theory on the construction of optimal truncated Low-Dimensional Dynamical Systems (LDDSs) with different physical meanings has been developed. The physical properties of the optimal bases are reflected in the user-defined optimal conditions. Through the analysis of linear and nonlinear examples, it is shown that the LDDSs constructed by using the Proper Orthogonal Decomposition (POD) method are not the optimum. After comparing the errors of LDDSs based on the new theory, POD and Fourier methods, it is concluded that the LDDSs based on the new theory are optimally truncated and catch the desired physical properties of the systems. The project supported by the National Natural Science Foundation of China and LNM, Institute of Mechanics, CAS