{"c9ff784e6a0440b80b45055fa2c9df7emhartmann":{"DOI":"","ISBN":"","ISSN":"","URL":"http://www.ifac-papersonline.net/","abstract":"This work is concerned with derivation of fully offine/online decomposable\n\teffcient aposteriori error estimators for reduced parameterized nonlinear\n\tkernel-based systems. The dynamical systems under consideration consist\n\tof a nonlinear, time- and parameter-dependent kernel expansion representing\n\tthe system's inner dynamics as well as time- and parameter-affne\n\tinputs, initial conditions and outputs. The estimators are established\n\tfor a reduction technique originally proposed in [7] and are an extension\n\tof the estimators derived in [11] to the fully time-dependent, parameterized\n\tsetting. Key features for the effcient error estimation are to use\n\tlocal Lipschitz constants provided by a certain class of kernels\n\tand an iterative scheme to balance computation cost against estimation\n\tsharpness. Together with the affnely time/parameter-dependent system\n\tcomponents a full offine/online decomposition for both the reduction\n\tprocess and the error estimators is possible. Some experimental results\n\tfor synthetic systems illustrate the effcient evaluation of the derived\n\terror estimators for different parameters.","annote":"","author":[{"family":"Wirtz","given":"Daniel"},{"family":"Haasdonk","given":"Bernard"}],"citation-label":"wirtz2012aposteriori","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical\n\tModelling","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"c9ff784e6a0440b80b45055fa2c9df7emhartmann","interhash":"e6dce191069323c30bda8a87cce2913a","intrahash":"c9ff784e6a0440b80b45055fa2c9df7e","issue":"","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"subspace error dynamical kernel a-posteriori methods, systems, nonlinear offline/online decomposition, parameterized projection estimates, model vorlaeufig reduction,","misc":{"owner":"haasdonk"},"note":"","number":"","page":"","page-first":"","publisher":"","publisher-place":"","status":"","title":"A-posteriori error estimation for parameterized kernel-based systems","type":"paper-conference","username":"mhartmann","version":"","volume":""},"699c9caf6155e0598d9c980105b8118dmhartmann":{"DOI":"10.1016/j.sysconle.2011.10.012","ISBN":"","ISSN":"","URL":"http://www.sciencedirect.com/science/article/pii/S0167691111002672","abstract":"In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. Numerical experiments\n\tdemonstrate the estimation improvement over different estimator versions\n\tand the rigor and effectiveness of the error bounds.","annote":"","author":[{"family":"Wirtz","given":"D."},{"family":"Haasdonk","given":"B."}],"citation-label":"wirtz2012efficient","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Systems and Control Letters","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"699c9caf6155e0598d9c980105b8118dmhartmann","interhash":"e80ae72fe2c1f9f79f4f7f8f5ce00735","intrahash":"699c9caf6155e0598d9c980105b8118d","issue":"1","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"subspace error dynamical kernel a-posteriori methods, systems, nonlinear offline/online decomposition, projection estimates, model vorlaeufig reduction,","misc":{"file":":/home/dwirtz/dwirtzwww/WH10_preprint.pdf:PDF","doi":"10.1016/j.sysconle.2011.10.012"},"note":"","number":"1","number-of-pages":"8","page":"203 - 211","page-first":"203","publisher":"","publisher-place":"","status":"","title":"Efficient a-posteriori error estimation for nonlinear kernel-based\n\treduced systems","type":"article-journal","username":"mhartmann","version":"","volume":"61"}}