On the application of time delay embedding for the data driven discovery of nonlinear systems from partial state information

Sriram Narayanan, Indranil Nayak, Mrinal Kumar

Abstract: Studying physical phenomena through data has become increasingly easy because of the abundance of information and improved computational infrastructure. However, the ability to understand and predict the behavior of such systems using limited data, owing to various reasons such as corrupted/unusable data or just the inability to capture certain types of information due to lack of sensors is emerging to be a central challenge in data science. In this paper, we propose to develop a technique that can reconstruct the entire dynamics of a nonlinear system from limited information. It is based on the method of time-delay embedding which is justified by Takens theorems and has demonstrated, with reasonable success, the reconstruction of low dimensional, non-linear systems purely from scalar time series. In this paper, we present initial ideas, methods, and observations.