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Mussmann_Thomas_15APR21_Thesis.pdf (1.4 MB)
ETD Abstract Container
Abstract Header
Data Driven Learning of Dynamical Systems Using Neural Networks
Author Info
Mussmann, Thomas Frederick
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1618589877977348
Abstract Details
Year and Degree
2021, Master of Mathematical Sciences, Ohio State University, Mathematical Sciences.
Abstract
We review general numerical approaches for discovering governing equations through data driven equation recovery. That is when the equations governing a dynamical system is unknown and depends on some hidden subset of variables. We review the structure of Neural Networks, Residual Neural Networks, and Recurrent Neural Networks. We also discuss the Mori Zwanzig formulation using history to substitute for hidden variables. We explore two examples, first is modeling Neuron Bursting with hidden variables using a Neural Network. Second, we examine particle traffic models and select one, which we dimensionally reduce and then attempt to predict future state from this dimensional reduction.
Committee
Dongbin Xiu (Advisor)
Dustin Mixon (Committee Member)
Pages
53 p.
Subject Headings
Mathematics
Keywords
data-driven discovery, neural network, traffic, Mori-Zwanzig formulation
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Citations
Mussmann, T. F. (2021).
Data Driven Learning of Dynamical Systems Using Neural Networks
[Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1618589877977348
APA Style (7th edition)
Mussmann, Thomas.
Data Driven Learning of Dynamical Systems Using Neural Networks.
2021. Ohio State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1618589877977348.
MLA Style (8th edition)
Mussmann, Thomas. "Data Driven Learning of Dynamical Systems Using Neural Networks." Master's thesis, Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1618589877977348
Chicago Manual of Style (17th edition)
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Document number:
osu1618589877977348
Download Count:
264
Copyright Info
© 2021, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.