Abstract
A nonparametric method assessing the error and variability margins in solutions depicted in a separated form using experimental results is illustrated in this work. The method assess the total variability of the solution including the modeling error and the truncation error when experimental results are available. The illustrated method is based on the use of the PGD separated form solutions, enriched by transforming a part of the PGD basis vectors into probabilistic one. The constructed probabilistic vectors are restricted to the physical solution’s Stiefel manifold. The result is a real-time parametric PGD solution enhanced with the solution variability and the confidence intervals.
Highlights
Nowadays, simulation-based decision making in engineering and sciences is widely accepted and used in predicting material and parts behavior
Many advanced methods for solving partial differential equation (PDE) are being designed to improve solution speed, aiming for real-time applications [4,11,13,30,37]. These techniques are commonly known by model order reduction techniques, mainly aiming at constructing a reduced basis for the solution of PDEs [22,40]
Regarding model order reduction techniques, the methods are divided into two large categories: (i) “a priori” model reduction techniques, which aims at constructing a solution in a reduced basis separated form, before having any knowledge of the full order model or the high definition model (HDM) solution [21,27]. (ii) “a posteriori” model reduction techniques, where the reduced order basis of projection is constructed from previous HDM solutions computed using efficient greedy algorithms to construct as accurate as Ghnatios and Barasinski Adv
Summary
Simulation-based decision making in engineering and sciences is widely accepted and used in predicting material and parts behavior. Many advanced methods for solving PDEs are being designed to improve solution speed, aiming for real-time applications [4,11,13,30,37]. These techniques are commonly known by model order reduction techniques (or model reduction techniques), mainly aiming at constructing a reduced basis for the solution of PDEs [22,40]. The PGD method appears to be the only “a priori” model reduction technique which is widely used nowadays to compute solutions in a fairly separable domain [10,25,26].
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