Establishment of a data-driven model reduction method for nonlinear dynamical systems with large degrees of freedom
In this research, we establish a method of model reduction. We reduce the dimensions of a system by extracting a small number of essential degrees of freedom from nonlinear dynamical phenomena with large degrees of freedom. We build a theoretical framework to perform this reduction based only on observation data, especially in situations where the basic equations of the system are unknown. We apply this to non-linear dynamical systems with large degrees of freedom, such as fluid systems, chemical reaction systems, quantum dissipative systems, and power engineering systems, and extract the mechanisms behind these phenomena in a way that is easy to comprehend. We also build a base for the development of new control and optimization methods for systems with large degrees of freedom based on reduced models. We develop the methodology by working simultaneously on the forward and backward problems for nonlinear dynamical systems with large degrees of freedom and linking them together and then establish a platform for their model reduction.
In this group, we consider chemical reaction systems or fluid systems with large degrees of freedom, basic physicochemical phenomena, such as quantum dissipative systems, and man-made non-linear phenomena with large degrees of freedom, such as power engineering systems. We reduce the dimensions of the system significantly by extracting a small number of variables that are essentially important to describe the phenomenon, and we aim to establish a model reduction method for nonlinear dynamical systems with large degrees of freedom that can lead to a development law. The keys to this research group are the dimension reduction theory of dynamical systems that has been developed in the field of nonlinear dynamics, the Koopman operator theory, which has been proposed recently in the field of applied mathematics and has attracted much attention, and the analysis method for dynamical systems based on dynamic mode decomposition in addition to a machine learning method to fuse them all together in an appropriate manner. This group deals with the representative group, which develops statistical science and machine learning infrastructure, and with the mathematics group, which develops the mathematical foundation for operator-theoretic analysis methods. Based on the knowledge of these two groups and by working with the biological modelling group that deals with life phenomena, we implement a complex dynamics computational platform based on operator-theoretic data analysis for specific physical phenomena, and we reveal its usefulness.