Learning the tangent space of dynamical instabilities from data
Name
1907.10413.pdf
Description
Accepted version
Size
1.16 MB
Format
Adobe PDF
Checksum (MD5)
ee90436705bd9c6a6e54c4a39f28235d
Author(s)
Blanchard, Antoine
Sapsis, Themistoklis P
Date Issued
2019
Journal
Chaos
Publisher
AIP Publishing
Version
Author's final manuscript
Abstract
For a large class of dynamical systems, the optimally time-dependent (OTD) modes, a set of deformable orthonormal tangent vectors that track directions of instabilities along any trajectory, are known to depend "pointwise" on the state of the system on the attractor but not on the history of the trajectory. We leverage the power of neural networks to learn this "pointwise" mapping from the phase space to OTD space directly from data. The result of the learning process is a cartography of directions associated with strongest instabilities in the phase space. Implications for data-driven prediction and control of dynamical instabilities are discussed.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1063/1.5120830
