Neural ODEs constrained by the gradient of a jointly learned maximal Lyapunov function universally approximate locally exponentially stable dynamics within a region of attraction exactly given by the Lyapunov 1-sublevel set.
(un)supervised learning of maximal lyapunov functions,
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math.OC 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
A neural Lyapunov architecture based on the log map and Zubov characterization is proposed for learning maximal regions of attraction on SO(n), with explicit derivative formulas enabling a two-phase training algorithm.
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Locally Stable Neural ODEs with Characterized Region of Attraction
Neural ODEs constrained by the gradient of a jointly learned maximal Lyapunov function universally approximate locally exponentially stable dynamics within a region of attraction exactly given by the Lyapunov 1-sublevel set.
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Learning Neural Maximal Lyapunov Functions on $\mathsf{SO}(n)$
A neural Lyapunov architecture based on the log map and Zubov characterization is proposed for learning maximal regions of attraction on SO(n), with explicit derivative formulas enabling a two-phase training algorithm.