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Goal-oriented adaptive sampling for projection-based reduced-order models

COMPUTERS & FLUIDS 2025年 290卷

作者： Blais, Donovan Nadarajah, Siva Biondic, Calista McGill Univ Dept Mech Engn 817 Rue Sherbrooke Ouest 270 Montreal PQ H3A 0C3 Canada

Modern aircraft design involves a large number of design parameters from a multitude of disciplines. Obtaining high-fidelity solutions for all combinations of such parameters is computationally unfeasible. Although the solution to a large-scale system of equations is generally an element of a large-dimensional space, the solution may actually lie on a reduced-order subspace induced by parameter variation. In order to capture this subspace, samples of the high-dimensional system called snapshots are used to build a reduced-order model. These models have generated interest as a means to compute high-fidelity solutions at a much lower computational cost. However, little value can be placed in a reduced-order solution without some quantification of its error. The dual-weighted residual can be used to obtain error estimates between the outputs of different models. Using dual-weighted residual error estimates in conjunction with a radial basis function interpolation, this work introduces a novel adaptive sampling method that chooses snapshots iteratively such that a prescribed output error tolerance is estimated to be met on the entirety of a parameter space. The adaptive sampling procedure is demonstrated on a one-dimensional Burgers' equation and two-dimensional inviscid flows.

关键词： Proper orthogonal decomposition (POD) Petrov-Galerkin projection projection-based model Reduced-order model (ROM) Adaptive sampling Error estimation

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