Christopher Curtis, San Diego State University
Will present a talk entitled:
Learning Dynamics through Dynamic Mode Decomposition
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. In this talk, 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. In particular, we present a neural networks based method by which one can learn how to generate accurate phase space trajectories using the DMD and data alone. We show our method is successful across a range of classic problems in dynamical systems, and we will also show preliminary results using our method to model ionospheric dynamics. Thus, through the use of modern machine learning techniques, we show 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.
SC166
Friday, March 4, 2022
12:00 pm
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C3S2 Clarkson Center for Complex Systems Science l http://webspace.clarkson.edu/~ebollt/Website-C3S2/index.html
CLARKSON UNIVERSITY l Potsdam, New York 13699-5720