Abstract
Uncertainty Quantification (UQ) is an important field to quantify the propagation of uncertainties, analyze sensitivities or realize statistical inversion of a mathematical model. Sampling-based estimation techniques evaluate the model for many different parameter samples. For computationally intensive models, this might require long runtimes or even be infeasible. This so-called multi-query problem can be speeded up or even be enabled with surrogate models from model order reduction (MOR) techniques. For accurate and physically consistent MOR, structure-preserving reduction is essential.
We investigate numerically how so-called symplectic model reduction techniques can improve the UQ results for Hamiltonian systems compared to conventional (non-symplectic) approaches. We conclude that the symplectic methods give better results and more robustness with respect to the size of the reduced model.
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https://www.morepas.org/software/rbmatlab/, last accessed: 30. Oct. 2019.
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Acknowledgements
We highly acknowledge the funding within the Soft Tissue Project (GRK 2198/1) and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2075—390740016. The valuable input of the anonymous reviewers is acknowledged.
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Buchfink, P., Haasdonk, B. (2021). Experimental Comparison of Symplectic and Non-symplectic Model Order Reduction on an Uncertainty Quantification Problem. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_19
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