What is it about?
Very often one numerical experiment in, say, computational fluid dynamics or aerodynamics, takes 1 week or 1 months. To compute statistical moments, risks, probabilities, the worst case scenario we need thousands of numerical tests (with different parameters). One of the options to make these experiments feasible is to use low-cost surrogate models (say, linear or quadratic approximations of the unknown solution). If the solution (and the problem) is multi-dimensional, i.e., depends on many parameters, then low-rank tensor techniques may help to reduce the cost further. In this work, we use low-rank tensor techniques to compress snapshots (solutions of the Navies - Stockes problem ) and then to compute statistical moments of the solution.
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Why is it important?
Low-cost surrogate replaces expensive physical model. It is easy to sample and to integrate. Low-rank tensor techniques allows us to reduce the computing time and the storage cost.
Perspectives
With this surrogate techniques we will be able to solve engineering problems with much more parameters (at the beginning it is not clear which parameters are important and which not), include more parameters into sensitivity analysis, design better experiments.
Dr. Alexander Litvinenko
Rheinisch Westfalische Technische Hochschule Aachen
Read the Original
This page is a summary of: Sampling and Low-Rank Tensor Approximation of the Response Surface, January 2013, Springer Science + Business Media,
DOI: 10.1007/978-3-642-41095-6_27.
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