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arXiv Machine Learning By Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fern\'andez, Jun Liu

Learning Lyapunov Operators for Nonlinear Systems

Read the original on arXiv Machine Learning →

The paper investigates the Lyapunov solution operator, which maps a vector field to its corresponding Lyapunov function via a dissipation-based PDE. It proves that this operator is well-defined, unique, and continuous on compact subsets of the domain of attraction under exponential stability, enabling uniform approximation across families of nonlinear systems. Using Fourier Neural Operators, the authors demonstrate that a single trained operator can accurately approximate Lyapunov functions for parameterized dynamics, showcasing the potential of neural operators in stability analysis.

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