New symbolic regression approach discovers Lyapunov functions autonomously

In a June 2026 paper, Ilias Mitrai and Wentao Tang from an undisclosed institution present a novel data-driven method for discovering Lyapunov functions—mathematical tools that prove stability in control systems. Their approach frames the problem as a constrained self-supervised symbolic regression task, where the Lyapunov function is represented as an expression tree of fixed depth. The key innovation is that no a priori assumptions about the function’s form are needed; instead, the model learns a symbolic expression directly from system data while enforcing the classical Lyapunov stability conditions as constraints. The authors also developed a tailored branch-and-bound-and-check solver to efficiently handle the resulting combinatorial optimization. This makes the discovered function inherently interpretable, a critical advantage over black-box neural network based methods.

The technique is general-purpose and can be applied to any continuous dynamical system. In several case studies, the algorithm successfully discovered valid Lyapunov functions, outperforming existing symbolic regression baselines in terms of interpretability and reliability. This work bridges control theory and machine learning, offering a practical tool for engineers who need to verify system stability without manual derivation. While the method is still early-stage, its potential impact spans robotics, aerospace, and autonomous systems where stability guarantees are essential. The paper is available on arXiv (2606.10045) and is expected to influence future work on safe AI and control.