[Faculty] Fwd: [CSRC.COLLOQUIUM] "Dynamic Mode Decomposition in Dynamical Systems II - Multiple and Missing Scales"

[Jose Castillo]

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DATE:
*Friday, February 25, 2022*


TITLE:
*Dynamic Mode Decomposition in Dynamical Systems II - Multiple and Missing
Scales *



TIME:
*3:30-4:30PM*



LOCATION:
*In Person - GMCS 314*
or
Join Zoom Meeting -   https://SDSU.zoom.us/j/84471061245
<https://sdsu.zoom.us/j/84471061245>


SPEAKER/BIO:
*Christopher 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, by incorporating
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.  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:
*Ricardo Carretero*

Note: Videos of previous colloquium talks can be seen on the CSRC website
in the colloquium archive section or on the CSRC YouTube page here
<https://www.youtube.com/channel/UCN0ZEztlmyDqG2pm-Rle_Eg/feed>.






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