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Adaptive Sparse Interpolation Methods for Electromagnetic Field Computation with Random Input Data

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.-19.04.2018, [Conference or Workshop Item]

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.

Item Type: Conference or Workshop Item
Erschienen: 2018
Creators: Loukrezis, Dimitrios ; Römer, Ulrich ; De Gersem, Herbert
Title: Adaptive Sparse Interpolation Methods for Electromagnetic Field Computation with Random Input Data
Language: English
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.

Journal or Publication Title: Proceedings of the SIAM Conference on Uncertainty Quantification
Journal volume: 2018
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute of Electromagnetic Field Theory (from 01.01.2019 renamed Institute for Accelerator Science and Electromagnetic Fields)
18 Department of Electrical Engineering and Information Technology > Institute for Accelerator Science and Electromagnetic Fields
Event Title: 2018 SIAM Conference on Uncertainty Quantification
Event Location: Garden Grove, USA
Event Dates: 16.-19.04.2018
Date Deposited: 16 Feb 2021 10:05
Additional Information:

TEMF-Pub-DB TEMF002695

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