Creation of a complex dynamics computational platform based on operator-theoretic data analysis
In this group, we build a methodology to develop estimation methods in accordance with various situations and identify statistically significant dynamics by further developing the stochastic formulation of the dynamic mode decomposition and the theoretical systems related to stochastic dynamical systems. We also build a framework for prediction and learning through the relationship between the physical concepts and mathematical models obtained through the collaborative research of the Nonlinear Physics Group and the Mathematics Group. This is done by using the information on the dynamic characteristics extracted by the development methodology with the mathematical model in an integrated manner. Further, for each of these cases, we apply the constructed method to data from across multiple domains focusing on issues dealt with by the Biological Modelling Group and conduct practical studies on the acquisition of scientific knowledge and usefulness in prediction and learning for each of the methods.
In addition to summarising the execution of the entire research project, this group conducts research on the development and theoretical analysis of the methodology of the problem of "estimation" of the operator expression of nonlinear dynamical systems from a data-driven perspective. In achieving the goal of “construction of theory and technology that contribute to the creation of innovative information utilization methods incorporating mathematical concepts,” this group is positioned under the research objective of constructing a framework to incorporate the concepts of mathematics and mathematical sciences (using a statistical framework) and plays a central role in coordinating with other groups.