Develops verifiable error bounds for PINN solutions of Lyapunov and HJB PDEs that turn residual bounds into relative error bounds, certified value function bounds, and valid Lyapunov functions.
A generalization of Zubov’s method to perturbed systems.SIAM Journal on Control and Optimization, 40(2):496–515
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Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equations
Develops verifiable error bounds for PINN solutions of Lyapunov and HJB PDEs that turn residual bounds into relative error bounds, certified value function bounds, and valid Lyapunov functions.