[세미나] 문승주 박사님

Chaos Synchronization and data assimilation

#### 문승주 박사님 (서울대학교 기초과학연구원) #### 2021년 9월 28일 (화) 16:00 #### Zoom
#### Abstract Examples of synchronization, pervasive throughout the natural world, are often awe-inspiring because they tend to transcend our human intuition. Synchronization found in chaotic dynamical systems, of which the Lorenz ’63 system is a quintessential example, is even more surprising because the very defining features of chaos include sensitive dependence on initial conditions. In this talk, I will explore chaos synchronization in high-dimensional extensions of the Lorenz ’63 system. These systems are conceived from both physical and mathematical points of view, faithful to the original derivation of the Lorenz ’63 system out of the governing partial differential equations that describe two-dimensional Reyleigh-Benard convection. In particular, the (3N)- and (3N+2)-dimensional generalizations extend the Lorenz ’63 system to higher dimensions by including additional wavenumber modes, allowing the system to resolve smaller scale motions. These generalized Lorenz systems exhibit not only self-synchronization when two coupled systems are identical but also generalized synchronization when they are of different dimensions. It is emphasized that chaos synchronization between high- and low-dimensional Lorenz systems following these generalizations share some similarities with a conceptual understanding of data assimilation; namely, given a high-dimensional ‘true’ system and lower-dimensional ‘model’ system, the information transmitted from the true system to the model system can be taken as the ‘observations’. Following this conceptual framework, it is argued that the generalized Lorenz systems can serve as a testbed model for evaluating various data assimilation schemes and can stand out amongst other more widely used testbed models such as the Lorenz ’63 and ’96 systems. Preliminary testbed results for the ensemble Kalman filter scheme using a very simple setup involving the (3N)-dimensional Lorenz systems will be discussed.