MOR Seminar

Topic: Error-controlled sparse collocation of reduced order models and applications in uncertainty quantification for vibroacoustics

Abstract: This talk is concerned with efficient surrogate modeling of parametric vibroacoustic problems in the frequency domain. We consider both frequency and random parameters, where in particular random influences quickly lead to high-dimensional problems, which typically result in a high computational effort. Recently, the interpolation of local reduced order models (ROMs) is receiving increasing attention, in part because sparse collocation allows to tackle high-dimensional problems. In this case, in addition to finite element discretization errors, at least two sources of numerical error arise, which need to be controlled. For a fixed random parameter, we consider moment matching ROMs, where an adjoint problem is used to cheaply and accurately estimate the error. This in turn allows for an adaptive selection of the frequency snapshot locations and the ROM moment-matching order. We then collocate these local ROMs on a dimension-adaptive or locally refined sparse grid, where another adjoint problem is used for error control and adaptivity. Dimension-adaptive sparse grids can exploit a possible parameter anisotropy, whereas local refinement is needed for systems with low damping, where the response surfaces exhibit strong variations. Overall, we obtain a numerical method, which is applicable in high dimensions and which features a high degree of flexibility. Given a prescribed error budget, the different error contributions can be balanced by adjusting the local ROM sizes and collocation grid. We will demonstrate the accuracy of the estimators and the capabilities of the method with several examples with a focus on vibroacoustics and the computation of statistical moments and global sensitivities.

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