%0 Journal Article %1 wirtz2012efficient %A Wirtz, D. %A Haasdonk, B. %D 2012 %J Systems and Control Letters %K a-posteriori decomposition, dynamical error estimates, kernel methods, model nonlinear offline/online projection reduction, subspace systems, vorlaeufig %N 1 %P 203 - 211 %R 10.1016/j.sysconle.2011.10.012 %T Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems %U http://www.sciencedirect.com/science/article/pii/S0167691111002672 %V 61 %X 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 estimation improvement over different estimator versions and the rigor and effectiveness of the error bounds.

@article{wirtz2012efficient, abstract = {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 estimation improvement over different estimator versions and the rigor and effectiveness of the error bounds.}, added-at = {2018-07-20T10:54:15.000+0200}, author = {Wirtz, D. and Haasdonk, B.}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2699c9caf6155e0598d9c980105b8118d/mhartmann}, doi = {10.1016/j.sysconle.2011.10.012}, file = {:/home/dwirtz/dwirtzwww/WH10_preprint.pdf:PDF}, interhash = {e80ae72fe2c1f9f79f4f7f8f5ce00735}, intrahash = {699c9caf6155e0598d9c980105b8118d}, journal = {Systems and Control Letters}, keywords = {a-posteriori decomposition, dynamical error estimates, kernel methods, model nonlinear offline/online projection reduction, subspace systems, vorlaeufig}, number = 1, pages = {203 - 211}, timestamp = {2018-07-20T08:54:15.000+0200}, title = {Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems}, url = {http://www.sciencedirect.com/science/article/pii/S0167691111002672}, volume = 61, year = 2012 }