Symbolic transformers discover new Lyapunov functions for dynamical systems

Summary

Alfarano, Charton, and Hayat trained symbolic sequence-to-sequence transformers to generate Lyapunov functions for dynamical systems. In experiments on randomly generated polynomial and non-polynomial systems, the models produced explicit functions that passed external mathematical checks, exceeded the compared sum-of-squares solver on the tested systems, and found functions for cases outside the solver's reach.

AI role

Sequence-to-sequence transformers trained on synthetically generated problem-solution pairs proposed candidate Lyapunov functions that were checked with symbolic, numerical, and SMT-based verifiers.

Narrative role

This is an earlier peer-reviewed example of AI producing inspectable mathematical objects for a longstanding search problem, filling the gap between conjecture-generation systems and the later wave of language-model-generated research proofs.

Caveat

The work does not solve the general Lyapunov-function problem: experiments use bounded-size randomly generated systems, and verification for non-polynomial cases can be numerical or limited to a chosen region. The model's method is also not an interpretable general mathematical procedure.

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