PUMA publications for /group/simtech/kernelFri 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.Fri Jul 20 10:54:15 CEST 2018International Journal for Numerical Methods in Biomedical Engineeringe3095 cnm.3095jae3095Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods02018models, peripheral kernel simulations reduced mixed-dimension methods, blood simulations, stenosis, real-time dimensionally surrogate vorlaeufig flow Summary In this work, we consider two kinds of model reduction techniquesto simulate blood flow through the largest systemic arteries, where a stenosis is located in a peripheral artery i.e. in an artery that is located far away from the heart. For our simulations we place the stenosis in one of the tibial arteries belonging to the right lower leg (right post tibial artery). The model reduction techniques that are used are on the one hand dimensionally reduced models (1-Dand 0-D models, the so-called mixed-dimension model) and on the other hand surrogate models produced by kernel methods. Both methods are combined in such a way that the mixed-dimension models yield training data for the surrogate model, where the surrogate model is parametrisedby the degree of narrowing of the peripheral stenosis. By means of a well-trained surrogate model, we show that simulation data can be reproduced with a satisfactory accuracy and that parameter optimisation or state estimation problems can be solved in a very efficient way. Furthermore it is demonstrated that a surrogate model enables us to present after a very short simulation time the impact of a varying degree of stenosis on blood flow, obtaining a speedup of several orders over the full model.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.