Loukrezis, Dimitrios ; Römer, Ulrich ; De Gersem, Herbert (2018)
Adaptive Sparse Interpolation Methods for Electromagnetic Field Computation with Random Input Data.
2018 SIAM Conference on Uncertainty Quantification. Garden Grove, USA (16.04.2018-19.04.2018)
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Kurzbeschreibung (Abstract)

In many applications of science and engineering, time-or resource-demanding simulation models are often sub-stituted by inexpensive polynomial surrogates in order toenable computationally challenging tasks, e.g. optimiza-tion or uncertainty quantification studies of field mod-els. For such approaches, the surrogate model’s accu-racy is of critical importance. Moreover, in the case ofmany input parameters, the curse-of-dimensionality sub-stantially hampers the surrogate’s construction. State-of-the-art methods employ interpolation on adaptively con-structed sparse grids, typically based on Clenshaw-Curtis[B. Schieche,Unsteady Adaptive Stochastic CollocationMethods on Sparse Grids, TU Darmstadt, 2012] or, morerecently, Leja [A. Narayan and J.D. Jakeman,AdaptiveLeja Sparse Grid Constructions for Stochastic Collocationand High-Dimensional Approximation,SIAMJ.Sci.Com-put., 2014] nodes. These methods provide accurate surro-gate models, mitigating or altogether avoiding the curse-of-dimensionality, at the cost of a relatively small numberof unused original model evaluations. In this work, we shalluse a benchmark example from the field of computationalelectromagnetics in order to compare the aforementionedmethods with respect to computational cost and accuracy.Moreover, we will suggest enhancement approaches, aim-ing to reduce the costs caused by unused model evaluationsduring the surrogate model’s construction.

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