Learning Geometrically-Informed Lyapunov Functions with Deep Diffeomorphic RBF Networks

Samuel Tesfazgi, Leonhard Sprandl, Sandra Hirche
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3889-3897, 2025.

Abstract

The practical deployment of learning-based autonomous systems would greatly benefit from tools that flexibly obtain safety guarantees in the form of certificate functions from data. While the geometrical properties of such certificate functions are well understood, synthesizing them using machine learning techniques still remains a challenge. To mitigate this issue, we propose a diffeomorphic function learning framework where prior structural knowledge of the desired output is encoded in the geometry of a simple surrogate function, which is subsequently augmented through an expressive, topology-preserving state-space transformation. Thereby, we achieve an indirect function approximation framework that is guaranteed to remain in the desired hypothesis space. To this end, we introduce a novel approach to construct diffeomorphic maps based on RBF networks, which facilitate precise, local transformations around data. Finally, we demonstrate our approach by learning diffeomorphic Lyapunov functions from real-world data and apply our method to different attractor systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-tesfazgi25a, title = {Learning Geometrically-Informed Lyapunov Functions with Deep Diffeomorphic RBF Networks}, author = {Tesfazgi, Samuel and Sprandl, Leonhard and Hirche, Sandra}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3889--3897}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/tesfazgi25a/tesfazgi25a.pdf}, url = {https://proceedings.mlr.press/v258/tesfazgi25a.html}, abstract = {The practical deployment of learning-based autonomous systems would greatly benefit from tools that flexibly obtain safety guarantees in the form of certificate functions from data. While the geometrical properties of such certificate functions are well understood, synthesizing them using machine learning techniques still remains a challenge. To mitigate this issue, we propose a diffeomorphic function learning framework where prior structural knowledge of the desired output is encoded in the geometry of a simple surrogate function, which is subsequently augmented through an expressive, topology-preserving state-space transformation. Thereby, we achieve an indirect function approximation framework that is guaranteed to remain in the desired hypothesis space. To this end, we introduce a novel approach to construct diffeomorphic maps based on RBF networks, which facilitate precise, local transformations around data. Finally, we demonstrate our approach by learning diffeomorphic Lyapunov functions from real-world data and apply our method to different attractor systems.} }
Endnote
%0 Conference Paper %T Learning Geometrically-Informed Lyapunov Functions with Deep Diffeomorphic RBF Networks %A Samuel Tesfazgi %A Leonhard Sprandl %A Sandra Hirche %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-tesfazgi25a %I PMLR %P 3889--3897 %U https://proceedings.mlr.press/v258/tesfazgi25a.html %V 258 %X The practical deployment of learning-based autonomous systems would greatly benefit from tools that flexibly obtain safety guarantees in the form of certificate functions from data. While the geometrical properties of such certificate functions are well understood, synthesizing them using machine learning techniques still remains a challenge. To mitigate this issue, we propose a diffeomorphic function learning framework where prior structural knowledge of the desired output is encoded in the geometry of a simple surrogate function, which is subsequently augmented through an expressive, topology-preserving state-space transformation. Thereby, we achieve an indirect function approximation framework that is guaranteed to remain in the desired hypothesis space. To this end, we introduce a novel approach to construct diffeomorphic maps based on RBF networks, which facilitate precise, local transformations around data. Finally, we demonstrate our approach by learning diffeomorphic Lyapunov functions from real-world data and apply our method to different attractor systems.
APA
Tesfazgi, S., Sprandl, L. & Hirche, S.. (2025). Learning Geometrically-Informed Lyapunov Functions with Deep Diffeomorphic RBF Networks. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3889-3897 Available from https://proceedings.mlr.press/v258/tesfazgi25a.html.

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