28 citations · 61 across the 15 of their papers we have counts for
3 papers · 1 filter
A Globally Asymptotically Stable Planar Homogeneous Polynomial Vector Field With No Polynomial Lyapunov Function
Jun Liu, Maxwell Fitzsimmons
We disprove the conjecture that every globally asymptotically stable homogeneous polynomial vector field admits a homogeneous polynomial Lyapunov function. The counterexample is a…
Safe and Robust Domains of Attraction for Discrete-Time Systems: A Set-Based Characterization and Certifiable Neural Network Estimation
Mohamed Serry, Maxwell Fitzsimmons, Jun Liu
Analyzing nonlinear systems with attracting robust invariant sets (RISs) requires estimating their domains of attraction (DOAs). Despite extensive research, accurately characterizi…
Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees
Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández +1
Uncertainty quantification for partial differential equations is traditionally grounded in discretization theory, where solution error is controlled via mesh/grid refinement. Physi…