Work

Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers

Year: 2024

Type: conference-paper

Abstract: Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics. We consider a long-standing open problem in mathematics: discovering a Lyapunov function that ensures the global stability of a dynamical system. This problem has no known general solution, and algorithmic solvers only exist for some small polynomial systems. We propose a new method for generating synthetic training samples from random solutions, and show that sequence-to-sequence transformers trained on such datasets perform better than algorithmic solvers and humans on polynomial systems, and can discover new Lyapunov functions for non-polynomial systems.

Source: neural information processing systems

DOI: 10.52202/079017-2969

Authors: Alberto Alfarano, François Charton, Amaury Hayat

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Rutgers, The State University of New Jersey, Institut Polytechnique de Paris, Grand Équipement National De Calcul Intensif, Office of Advanced Research Computing, Rutgers, The State University of New Jersey

OpenAlex ID: W4415796507

FWCI: 35.69

Cites:

Cited by: 13

Related to: 10