Discovering Lyapunov functions with transformers

Alberto Alfarano, Francois Charton, Amaury Hayat

Keywords: transformers, mathematics, symbolic, calculus, open problem

TL;DR: We train transformers to discover Lyapunov functions, a longstanding open problem in mathematics.

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.

Submission Number: 13