Discovering Lyapunov functions with transformers
Alberto Alfarano · Francois Charton · Amaury Hayat
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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