PUMA publications for /user/mathematik/estimates,%20offline/online%20dynamicalWed Sep 29 14:35:08 CEST 2021Systems {\&} Control Letters1203--211Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems612012subspace error dynamical kernel a-posteriori from:britsteiner methods, ians nonlinear systems, offline/online decomposition, projection estimates, model anm reduction, 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.Fri Jul 20 10:55:02 CEST 2018Systems and Control Letters1203 - 211Efficient a-posteriori error estimation for nonlinear kernel-based
reduced systems612012a-posteriori decomposition, dynamical error estimates, from:mhartmann ians kernel methods, model nonlinear offline/online projection reduction, subspace systems, vorlaeufig 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.Fri Jul 20 10:54:37 CEST 2018Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical
ModellingA-posteriori error estimation for parameterized kernel-based systems2012a-posteriori decomposition, dynamical error estimates, from:mhartmann ians kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems, vorlaeufig 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.