Data-Driven Bifurcation Analysis via Learning of Homeomorphism
Abstract
This work proposes a data-driven approach for bifurcation analysis in nonlinear systems when the governing differential equations are not available. Specifically, regularized regression with barrier terms is used to learn a homeomorphism that transforms the underlying system to a reference linear dynamics — either an explicit reference model with desired qualitative behavior, or Koopman eigenfunctions that are identified from some system data under a reference parameter value. When such a homeomorphism fails to be constructed with low error, bifurcation phenomenon is detected. A case study is performed on a planar numerical example where a pitchfork bifurcation exists.
Cite
Text
Tang. "Data-Driven Bifurcation Analysis via Learning of Homeomorphism." Proceedings of the 6th Annual Learning for Dynamics & Control Conference, 2024.Markdown
[Tang. "Data-Driven Bifurcation Analysis via Learning of Homeomorphism." Proceedings of the 6th Annual Learning for Dynamics & Control Conference, 2024.](https://mlanthology.org/l4dc/2024/tang2024l4dc-datadriven/)BibTeX
@inproceedings{tang2024l4dc-datadriven,
title = {{Data-Driven Bifurcation Analysis via Learning of Homeomorphism}},
author = {Tang, Wentao},
booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference},
year = {2024},
pages = {1149-1160},
volume = {242},
url = {https://mlanthology.org/l4dc/2024/tang2024l4dc-datadriven/}
}