Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems

In this paper we consider the topic of model reduction for nonlinear dynamical systems based on kernel expansions. Our approach allows for a full offline/online decomposition and efficient online computation of the reduced model. In particular we derive an a-posteriori state-space error estimator for the reduction error. A key ingredient is a local Lipschitz constant estimation that enables rigorous a-posteriori error estimation. The computation of the error estimator is realized by solving an auxiliary differential equation during online simulations. Estimation iterations can be performed that allow a balancing between estimation sharpness and computation time. Numerical experiments demonstrate the rigour and effectiveness of the error bounds.