28 citations · 74 across the 24 of their papers we have counts for
5 papers · 1 filter
Universal Approximation of Maximal Lyapunov Functions with Anchored Neural Networks
Jun Liu
Maximal Lyapunov functions encode the entire domain of attraction of an asymptotically stable equilibrium, but preserving strict decrease under neural approximation is difficult be…
Generalizing Dynamics Modeling More Easily from Representation Perspective
Yiming Wang, Zhengnan Zhang, Genghe Zhang +7
Learning system dynamics from observations is a critical problem in many applications over various real-world complex systems, e.g., climate, ecology, and fluid systems. Recently,…
Verifiable Error Bounds for Physics-Informed Neural KKL Observers
Hannah Berin-Costain, Harry Wang, Kirsten Morris +1
This paper proposes a computable state-estimation error bound for learning-based Kazantzis--Kravaris/Luenberger (KKL) observers. Recent work learns the KKL transformation map with…
Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equations
Jun Liu
Many core problems in nonlinear systems analysis and control can be recast as solving partial differential equations (PDEs) such as Lyapunov and Hamilton-Jacobi-Bellman (HJB) equat…
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…