Comparative study of modal decomposition and dynamic equation reconstruction in data-driven modeling

Due to the increasing complexity of dynamic systems, it is increasingly difficult for traditional mathematical methods to meet the modeling requirements of complex dynamic systems. With the continuous innovation of computer and big data technologies, massive data can be easily obtained and stored. Therefore, studies of dynamic system modeling through data-driven approaches have attracted more and more researchers’ attention. This paper compares the dynamic mode decomposition method and dynamic equation reconstruction. Taking Lorenz and nonlinear Helmholtz resonant systems as examples, the two methods show the ability to reconstruct and describe the evolution characteristics of the dynamic system. Specifically, the dynamic mode decomposition method can describe the characteristics of the dynamic system more intuitively; however, it cannot provide physical insights. On the other hand, the discovery of dynamic equations from data can more accurately express the physical evolution characteristics of the dynamic system; however, it is easily affected by random noise. Because the dynamic mode decomposition method can obtain a reduced-order model, which can not only retain useful information of the original data but also reduce the noise disturbances, it can effectively improve the noise attenuation and finally reconstructions of differential dynamical equations.