%0 Conference Paper %1 wirtz2012aposteriori %A Wirtz, Daniel %A Haasdonk, Bernard %B Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling %D 2012 %K a-posteriori decomposition, dynamical error estimates, kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems, vorlaeufig %T A-posteriori error estimation for parameterized kernel-based systems %U http://www.ifac-papersonline.net/ %X This work is concerned with derivation of fully offine/online decomposable effcient aposteriori 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-affne inputs, initial conditions and outputs. The estimators are established for a reduction technique originally proposed in [7] and are an extension of the estimators derived in [11] to the fully time-dependent, parameterized setting. Key features for the effcient 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 affnely time/parameter-dependent system components a full offine/online decomposition for both the reduction process and the error estimators is possible. Some experimental results for synthetic systems illustrate the effcient evaluation of the derived error estimators for different parameters.

@inproceedings{wirtz2012aposteriori, abstract = {This work is concerned with derivation of fully offine/online decomposable effcient aposteriori 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-affne inputs, initial conditions and outputs. The estimators are established for a reduction technique originally proposed in [7] and are an extension of the estimators derived in [11] to the fully time-dependent, parameterized setting. Key features for the effcient 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 affnely time/parameter-dependent system components a full offine/online decomposition for both the reduction process and the error estimators is possible. Some experimental results for synthetic systems illustrate the effcient evaluation of the derived error estimators for different parameters.}, added-at = {2018-07-20T10:54:15.000+0200}, author = {Wirtz, Daniel and Haasdonk, Bernard}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2c9ff784e6a0440b80b45055fa2c9df7e/mhartmann}, booktitle = {Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling}, interhash = {e6dce191069323c30bda8a87cce2913a}, intrahash = {c9ff784e6a0440b80b45055fa2c9df7e}, keywords = {a-posteriori decomposition, dynamical error estimates, kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems, vorlaeufig}, owner = {haasdonk}, timestamp = {2018-07-20T08:54:15.000+0200}, title = {A-posteriori error estimation for parameterized kernel-based systems}, url = {http://www.ifac-papersonline.net/}, year = 2012 }