Topological Dynamics via Learned Hybrid Systems

Bernardo Rivas, William Kalies, Kaito Iwasaki, Anthony Bloch, Maani Ghaffari
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1663-1674, 2026.

Abstract

The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley’s index theory have provided a rigorous framework for this analysis. However, the computation relies on rigorous outer approximations of the dynamics over a discretized state space, which is challenging to obtain from scattered trajectory data. We propose a methodology that integrates recent advances in switching system identification via convex optimization to bridge this gap between data and topological analysis. We leverage the identified switching system to construct combinatorial outer approximations. This paper outlines the integration of these methods and evaluates the efficacy of computing Morse graphs versus data-driven and statistical approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-rivas26a, title = {Topological Dynamics via Learned Hybrid Systems}, author = {Rivas, Bernardo and Kalies, William and Iwasaki, Kaito and Bloch, Anthony and Ghaffari, Maani}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1663--1674}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/rivas26a/rivas26a.pdf}, url = {https://proceedings.mlr.press/v331/rivas26a.html}, abstract = {The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley’s index theory have provided a rigorous framework for this analysis. However, the computation relies on rigorous outer approximations of the dynamics over a discretized state space, which is challenging to obtain from scattered trajectory data. We propose a methodology that integrates recent advances in switching system identification via convex optimization to bridge this gap between data and topological analysis. We leverage the identified switching system to construct combinatorial outer approximations. This paper outlines the integration of these methods and evaluates the efficacy of computing Morse graphs versus data-driven and statistical approaches.} }
Endnote
%0 Conference Paper %T Topological Dynamics via Learned Hybrid Systems %A Bernardo Rivas %A William Kalies %A Kaito Iwasaki %A Anthony Bloch %A Maani Ghaffari %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-rivas26a %I PMLR %P 1663--1674 %U https://proceedings.mlr.press/v331/rivas26a.html %V 331 %X The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley’s index theory have provided a rigorous framework for this analysis. However, the computation relies on rigorous outer approximations of the dynamics over a discretized state space, which is challenging to obtain from scattered trajectory data. We propose a methodology that integrates recent advances in switching system identification via convex optimization to bridge this gap between data and topological analysis. We leverage the identified switching system to construct combinatorial outer approximations. This paper outlines the integration of these methods and evaluates the efficacy of computing Morse graphs versus data-driven and statistical approaches.
APA
Rivas, B., Kalies, W., Iwasaki, K., Bloch, A. & Ghaffari, M.. (2026). Topological Dynamics via Learned Hybrid Systems. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1663-1674 Available from https://proceedings.mlr.press/v331/rivas26a.html.

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