Author

Maxwell Fitzsimmons

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#machine learning Preprint Sep 2026

Learning Lyapunov Operators for Nonlinear Systems

Constructing Lyapunov functions for nonlinear dynamical systems is a central problem in stability analysis, yet remains challenging. Lyapunov functions are commonly characterized as solutions to first-order partial differential equations (PDEs), but these solutions are typically obtained for single systems, limiting th...

Amartya Mukherjee, Maxwell Fitzsimmons, D. C. Del Rey Fernández et al. · 0 citations

#machine learning Mar 2026

Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees

It is proved that when neural approximations lie in a compact subset of the solution space, vanishing residual error guarantees convergence to the true solution.

Amartya Mukherjee, Maxwell Fitzsimmons, D. C. Del Rey Fernández et al. · arXiv.org · 1 citation