@inproceedings{
alfarano2023discovering,
title={Discovering Lyapunov functions with transformers},
author={Alberto Alfarano and Francois Charton and Amaury Hayat},
booktitle={The 3rd Workshop on Mathematical Reasoning and AI at NeurIPS'23},
year={2023},
url={https://openreview.net/forum?id=1dD5cJCida}
}
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.
Discovering Lyapunov functions with transformers
Alberto Alfarano Francois Charton Amaury Hayat