Minisymposium (ID: SS-DDMDS)

Data-Driven Methods For Dynamical Systems

Dimitris Giannakis (New York University), Tyrus Berry (Penn State University)

Large-scale datasets generated by dynamical systems are ubiquitous in science and engineering. Acquired via observational networks or generated by numerical models, these datasets have an important special structure, namely that the samples occur with a time ordering which is the outcome of a deterministic or stochastic dynamical system. There exists a strong need for data analysis algorithms to leverage the information content in the data, leading to advances in problems such as dimension reduction, prediction, and uncertainty quantification. While the data is extrinsically high-dimensional, in many applications there is evidence that the data lies near a low-dimensional structure, nonlinearly embedded in the ambient space. Modern nonlinear methods leverage these coarse geometric structures using tools such as localizing kernels, multiscale bases, or the discrete exterior calculus to represent the geometry. The aim of this special session is to bring together an interdisciplinary group of researchers to discuss recent developments in these topics, having as a common theme the nonlinear, discrete geometry of dynamical system data.