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From Data to Uncertainty: An Efficient Integrated Data-Driven Sparse Grid Approach to Propagate Uncertainty

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Sparse Grids and Applications - Stuttgart 2014

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 109))

Abstract

We present a novel data-driven approach to propagate uncertainty. It consists of a highly efficient integrated adaptive sparse grid approach. We remove the gap between the subjective assumptions of the input’s uncertainty and the unknown real distribution by applying sparse grid density estimation on given measurements. We link the estimation to the adaptive sparse grid collocation method for the propagation of uncertainty. This integrated approach gives us two main advantages: First, the linkage of the density estimation and the stochastic collocation method is straightforward as they use the same fundamental principles. Second, we can efficiently estimate moments for the quantity of interest without any additional approximation errors. This includes the challenging task of solving higher-dimensional integrals. We applied this new approach to a complex subsurface flow problem and showed that it can compete with state-of-the-art methods. Our sparse grid approach excels by efficiency, accuracy and flexibility and thus can be applied in many fields from financial to environmental sciences.

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Acknowledgements

The authors acknowledge the German Research Foundation (DFG) for its financial support of the project within the Cluster of Excellence in Simulation Technology at the University of Stuttgart.

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Authors and Affiliations

  1. Department of Simulation Software Engineering, IPVS, University of Stuttgart, Stuttgart, Germany

    Fabian Franzelin & Dirk Pflüger

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  1. Fabian Franzelin
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  2. Dirk Pflüger
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Correspondence to Fabian Franzelin .

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Editors and Affiliations

  1. Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

    Jochen Garcke

  2. Institute for Parallel and Distributed S, Universität Stuttgart, Stuttgart, Germany

    Dirk Pflüger

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Franzelin, F., Pflüger, D. (2016). From Data to Uncertainty: An Efficient Integrated Data-Driven Sparse Grid Approach to Propagate Uncertainty. In: Garcke, J., Pflüger, D. (eds) Sparse Grids and Applications - Stuttgart 2014. Lecture Notes in Computational Science and Engineering, vol 109. Springer, Cham. https://doi.org/10.1007/978-3-319-28262-6_2

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