Abstract
AbstractThis work is concerned with derivation of fully offline/online decomposable efficient a-posteriori error estimators for reduced parameterized nonlinear kernel-based systems. The dynamical systems under consideration consist of a nonlinear, time- and parameter-dependent kernel expansion representing the system's inner dynamics as well as time- and parameter-affine inputs, initial conditions and outputs. The estimators are established for a reduction technique originally proposed in Phillips et al. (2003) and are an extension of the estimators derived in Wirtz and Haasdonk (2012) to the fully time-dependent, parameterized setting. Key features for the efficient error estimation are to use local Lipschitz constants provided by a certain class of kernels and an iterative scheme to balance computation cost against estimation sharpness. Together with the affinely time/parameter-dependent system components a full offline/online decomposition for both the reduction process and the error estimators is possible. Some experimental results for synthetic systems illustrate the efficient evaluation of the derived error estimators for different parameters.
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