DATE:

Friday, December 3, 2021

TIME:

3:30 PM

LOCATION:

GMCS 314

SPEAKER:

Christopher W. Curtis, Mathematics and Statistics, San Diego State University

ABSTRACT:

Much of applied mathematics has seen a recent shift in focus towards analyzing and describing measured time series as opposed to more traditional practices such as exploring particular systems of equations. This reflects a modern reality in which measurements are far easier to come by than more sophisticated mathematical models. Therefore developing model free, data focused tools for dynamical systems has become a major subject of much contemporary interest. We will explore how one such tool, the Dynamic Mode Decomposition (DMD), can be coupled with several other mathematical methods to facilitate sophisticated data analysis and prediction without the need for model equations. First, via a coupling ot wavelet analysis, we show how the DMD can be used to analyze and ultimately predict complex multiscale ionospheric plasma dynamics. Then, using the Mori-Zwanzig formalism of nonequilibrium statistical mechanics, we present a method by which the DMD method can be extended to cope with missing data in a physically consistent, yet still model free way. Finally, using neural networks, we develop a method by which one can learn how to generate accurate phase space trajectories using the DMD and data alone. While much of our work is preliminary, it nevertheless shows a very promising future for the DMD as a fundamental framework in building accurate and complex data based models which should provide readily usable tools in a wide range of physically motivated problem areas.

HOST:

Jose Castillo

VIDEO: