Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems |
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Authors: | D Wirtz B Haasdonk |
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Affiliation: | Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany |
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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. |
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Keywords: | Nonlinear dynamical systems Model reduction Kernel methods a-posteriori error estimates Offline/online decomposition Subspace projection |
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