In:
ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, Vol. 52, No. 2 ( 2018-3), p. 705-728
Abstract:
The main result of this paper gives a numerically efficient method to bound the error that is made when approximating the output of a nonlinear problem depending on an unknown parameter (described by a probability distribution). The class of nonlinear problems under consideration includes high-dimensional nonlinear problems with a nonlinear output function. A goal-oriented probabilistic bound is computed by considering two phases. An offline phase dedicated to the computation of a reduced model during which the full nonlinear problem needs to be solved only a small number of times. The second phase is an online phase which approximates the output. This approach is applied to a toy model and to a nonlinear partial differential equation, more precisely the Burgers equation with unknown initial condition given by two probabilistic parameters. The savings in computational cost are evaluated and presented.
Type of Medium:
Online Resource
ISSN:
0764-583X
,
1290-3841
DOI:
10.1051/m2an/2018003
Language:
English
Publisher:
EDP Sciences
Publication Date:
2018
detail.hit.zdb_id:
2659525-4
detail.hit.zdb_id:
1485131-3
SSG:
11
SSG:
3,2
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