AI RESEARCH
Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equations
arXiv CS.LG
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ArXi:2603.19545v1 Announce Type: cross Many core problems in nonlinear systems analysis and control can be recast as solving partial differential equations (PDEs) such as Lyapuno and Hamilton-Jacobi-Bellman (HJB) equations. Physics-informed neural networks (PINNs) have emerged as a promising mesh-free approach for approximating their solutions, but in most existing works there is no rigorous guarantee that a small PDE residual implies a small solution error.