Discovering Lyapunov Functions with Transformers

Abstract

We consider a long-standing open problem in mathematics: discovering the Lyapunov functions that control the global stability of dynamical systems. We propose a method for generating training data, and train sequence-to-sequence transformers to predict the Lyapunov functions of polynomial and non-polynomial systems with high accuracy. We also introduce a new baseline for this problem, and show that our models achieve state-of-the-art results, and outperform approximation based techniques and sum-of-square algorithmic routines.

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Cite

Text

Alfarano et al. "Discovering Lyapunov Functions with Transformers." NeurIPS 2023 Workshops: MATH-AI, 2023.

Markdown

[Alfarano et al. "Discovering Lyapunov Functions with Transformers." NeurIPS 2023 Workshops: MATH-AI, 2023.](https://mlanthology.org/neuripsw/2023/alfarano2023neuripsw-discovering/)

BibTeX

@inproceedings{alfarano2023neuripsw-discovering,
  title     = {{Discovering Lyapunov Functions with Transformers}},
  author    = {Alfarano, Alberto and Charton, Francois and Hayat, Amaury},
  booktitle = {NeurIPS 2023 Workshops: MATH-AI},
  year      = {2023},
  url       = {https://mlanthology.org/neuripsw/2023/alfarano2023neuripsw-discovering/}
}