https://puma.ub.uni-stuttgart.de/group/simtech/kernel%20errorPUMA RSS feed for /group/simtech/kernel%20error2026-04-21T18:18:55+02:00https://puma.ub.uni-stuttgart.de/bibtex/2c9ff784e6a0440b80b45055fa2c9df7e/mhartmannmhartmann2018-07-20T10:54:15+02:00subspace error dynamical kernel a-posteriori methods, systems, nonlinear offline/online decomposition, parameterized projection estimates, model vorlaeufig reduction, <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Daniel Wirtz" itemprop="url" href="/person/1e6dce191069323c30bda8a87cce2913a/author/0"><span itemprop="name">D. Wirtz</span></a></span>, </span> und <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Bernard Haasdonk" itemprop="url" href="/person/1e6dce191069323c30bda8a87cce2913a/author/1"><span itemprop="name">B. Haasdonk</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/Book" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="name">Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling</span>, </em></span>(<em><span>2012<meta content="2012" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:15 CEST 2018Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical ModellingA-posteriori error estimation for parameterized kernel-based systems2012subspace error dynamical kernel a-posteriori methods, systems, nonlinear offline/online decomposition, parameterized projection estimates, model vorlaeufig reduction, 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.https://puma.ub.uni-stuttgart.de/bibtex/2699c9caf6155e0598d9c980105b8118d/mhartmannmhartmann2018-07-20T10:54:15+02:00subspace error dynamical kernel a-posteriori methods, systems, nonlinear offline/online decomposition, projection estimates, model vorlaeufig reduction, <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="D. Wirtz" itemprop="url" href="/person/1e80ae72fe2c1f9f79f4f7f8f5ce00735/author/0"><span itemprop="name">D. Wirtz</span></a></span>, </span> und <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="B. Haasdonk" itemprop="url" href="/person/1e80ae72fe2c1f9f79f4f7f8f5ce00735/author/1"><span itemprop="name">B. Haasdonk</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="journal">Systems and Control Letters</span>, </em> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">61 </span></span>(<span itemprop="issueNumber">1</span>): <span itemprop="pagination">203 - 211</span></em> </span>(<em><span>2012<meta content="2012" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:15 CEST 2018Systems and Control Letters1203 - 211Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems612012subspace error dynamical kernel a-posteriori methods, systems, nonlinear offline/online decomposition, projection estimates, model vorlaeufig 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.