Data-driven bifurcation analysis via learning of homeomorphism

Wentao Tang
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:1149-1160, 2024.

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 this Paper

BibTeX
@InProceedings{pmlr-v242-tang24b, title = {Data-driven bifurcation analysis via learning of homeomorphism}, author = {Tang, Wentao}, booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference}, pages = {1149--1160}, year = {2024}, editor = {Abate, Alessandro and Cannon, Mark and Margellos, Kostas and Papachristodoulou, Antonis}, volume = {242}, series = {Proceedings of Machine Learning Research}, month = {15--17 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v242/tang24b/tang24b.pdf}, url = {https://proceedings.mlr.press/v242/tang24b.html}, 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.} }
Endnote
%0 Conference Paper %T Data-driven bifurcation analysis via learning of homeomorphism %A Wentao Tang %B Proceedings of the 6th Annual Learning for Dynamics & Control Conference %C Proceedings of Machine Learning Research %D 2024 %E Alessandro Abate %E Mark Cannon %E Kostas Margellos %E Antonis Papachristodoulou %F pmlr-v242-tang24b %I PMLR %P 1149--1160 %U https://proceedings.mlr.press/v242/tang24b.html %V 242 %X 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.
APA
Tang, W.. (2024). Data-driven bifurcation analysis via learning of homeomorphism. Proceedings of the 6th Annual Learning for Dynamics & Control Conference, in Proceedings of Machine Learning Research 242:1149-1160 Available from https://proceedings.mlr.press/v242/tang24b.html.

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