Poster
in
Workshop: MATH-AI: The 3rd Workshop on Mathematical Reasoning and AI
Discovering Lyapunov functions with transformers
Alberto Alfarano · Francois Charton · Amaury Hayat
Keywords: [ transformers ] [ open problem ] [ calculus ] [ mathematics ] [ Symbolic ]
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.