Non intrusive method for parametric model order reduction using a bi-calibrated interpolation on the Grassmann manifold

Oulghelou, Mourad; Allery, Cyrille

doi:10.1016/j.jcp.2020.109924

Cited by 18 publications

(12 citation statements)

References 31 publications

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“…These calibration matrices are a solution to an optimization problem under constraints whose solution is analytically determined. For more details, see [23,24].…”

Section: Description Of the Bi-citsgm Methodsmentioning

confidence: 99%

“…Moreover, derivative operators are difficult to assess using a commercial CFD code. Consequently, in this paper, we use the non-intrusive method Bi-CITSGM [23,45].…”

Section: Definition Of Reduced Basesmentioning

confidence: 99%

“…From some CFD calculations of flow through a Representative Elementary Volume (REV) of the tube bundle, pressure and velocity fields were decomposed by POD (Proper Orthogonal Decomposition). Then, the non-intrusive reduced model method, Bi-CITSGM (Bi-Calibrated Interpolation on the Tangent Subspace of the Grassmann Manifold) [23,24], was applied in order to determine the solution for a new parameter. In this method, spatial and temporal POD sampling bases are interpolated by ITSGM (Interpolation on the Tangent Subspace of the Grassmann Manifold) [25] and the temporal eigenvalues by usual methods such as Lagrange, IDW (Inverse Distance Weighting), or RBF (Radial Basis Function).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical Prediction of Two-Phase Flow through a Tube Bundle Based on Reduced-Order Model and a Void Fraction Correlation

Dubot

Allery

Melot

et al. 2021

Entropy

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Predicting the void fraction of a two-phase flow outside of tubes is essential to evaluate the thermohydraulic behaviour in steam generators. Indeed, it determines two-phase mixture properties and affects two-phase mixture velocity, which enable evaluating the pressure drop of the system. The two-fluid model for the numerical simulation of two-phase flows requires interaction laws between phases which are not known and/or reliable for a flow within a tube bundle. Therefore, the mixture model, for which it is easier to implement suitable correlations for tube bundles, is used. Indeed, by expressing the relative velocity as a function of slip, the void fraction model of Feenstra et al.and Hibiki et al. developed for upward cross-flow through horizontal tube bundles is introduced and compared. With the method suggested in this paper, the physical phenomena that occur in tube bundles are taken into consideration. Moreover, the tube bundle is modelled using a porous media approach where the Darcy–Forchheimer term is usually defined by correlations found in the literature. However, for some tube bundle geometries, these correlations are not available. The second goal of the paper is to quickly compute, in quasi-real-time, this term by a non-intrusive parametric reduced model based on Proper Orthogonal Decomposition. This method, named Bi-CITSGM (Bi-Calibrated Interpolation on the Tangent Subspace of the Grassmann Manifold), consists in interpolating the spatial and temporal bases by ITSGM (Interpolation on the Tangent Subspace of the Grassmann Manifold) in order to define the solution for a new parameter. The two developed methods are validated based on the experimental results obtained by Dowlati et al. for a two-phase cross-flow through a horizontal tube bundle.

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“…These calibration matrices are a solution to an optimization problem under constraints whose solution is analytically determined. For more details, see [23,24].…”

Section: Description Of the Bi-citsgm Methodsmentioning

confidence: 99%

“…Moreover, derivative operators are difficult to assess using a commercial CFD code. Consequently, in this paper, we use the non-intrusive method Bi-CITSGM [23,45].…”

Section: Definition Of Reduced Basesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Prediction of Two-Phase Flow through a Tube Bundle Based on Reduced-Order Model and a Void Fraction Correlation

Dubot

Allery

Melot

et al. 2021

Entropy

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show abstract

“…Hence, the application of PODI is, in general, better suited when the number of parameters of interest is small, and becomes more challenging when N p is large. Note that more complex techniques, such as the interpolation on Grassmann manifolds, have been considered in the literature [1,30,43] demonstrating, for certain applications, a superior accuracy compared to classical interpolation techniques. The interpolation chosen in this work is the simplest choice and interpolation on Grassmann manifolds has the potential to offer an increased accuracy.…”

Section: Off-line Stage: Construction Of the Basis Via Svdmentioning

confidence: 99%

A combined reduced order‐full order methodology for the solution of 3D magneto‐mechanical problems with application to magnetic resonance imaging scanners

Seoane

Ledger

Gil

et al. 2020

Numerical Meth Engineering

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The design of a new MRI scanner requires multiple numerical simulations of the same magneto-mechanical problem for varying model parameters, such as frequency and electric conductivity, in order to ensure that the vibrations, noise and heat dissipation are minimized. The high computational cost required for these repeated simulations leads to a bottleneck in the design process due to an increased design time and, thus, a higher cost. To alleviate these issues, the application of reduced order modelling techniques, which are able to find a general solution to high dimensional parametric problems in a very efficient manner, is considered. Building on the established Proper Orthogonal Decomposition (POD) technique available in the literature, the main novelty of this work is an efficient implementation for the solution of 3D magnetomechanical problems in the context of challenging MRI configurations. This methodology provides a general solution for varying parameters of interest. The accuracy and efficiency of the method is proven by applying it to challenging MRI configurations and comparing with the full order solution.

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“…The ITSGM consists of five steps : (1) from the trained parametrized POD subspaces, chose a subspace to be the reference point of tangency to Grassmann manifold; (2) use the geodesic logarithm and map all the data points to the tangent space; (3) perform linear interpolation in the tangent space; (4) map back the result by the geodesic exponential to the Grassmann manifold; (5) perform Galerkin projections and solve the resulting system of ordinary differential equations. This interpolation methodology has been successfully applied in adaptation of reduced order models 31,32 adjoint based optimal control, 33 data‐driven optimal control, 34 and so on. In the same spirit of the ITSGM, a selection of methods were recently proposed.…”

Section: Introductionmentioning

confidence: 99%

Parametric reduced order models based on a Riemannian barycentric interpolation

Oulghelou

Allery

2021

Numerical Meth Engineering

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A new strategy for constructing parametric Galerkin reduced order models is presented in this article. This strategy is achieved thanks to the Riemannian manifold, quotient of the set of full-rank matrices by the orthogonal group.Starting from a set of training parametrized subspaces of the same dimension, namely obtained by the proper orthogonal decomposition, the projection subspace for a new untrained parameter value is sought as the Karcher barycenter of the data points. The principal advantage of this strategy is that it leads to parametric reduced order models that are naturally flexible with respect to parameter variations. This property is a result of the simple expressions of the geodesic exponential and logarithmic mappings involved in the calculations of the approximated projection subspace. Confrontation with the usual interpolation in the tangent space to the Grassmann manifold is carried out for the flow problem past a circular cylinder and the flow in a lid-driven cavity. Comparable results in terms of accuracy are obtained, while the proposed approach is shown to be computationally cheaper by allowing real-time update of Galerkin projections.

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Non intrusive method for parametric model order reduction using a bi-calibrated interpolation on the Grassmann manifold

Cited by 18 publications

References 31 publications

Numerical Prediction of Two-Phase Flow through a Tube Bundle Based on Reduced-Order Model and a Void Fraction Correlation

Numerical Prediction of Two-Phase Flow through a Tube Bundle Based on Reduced-Order Model and a Void Fraction Correlation

A combined reduced order‐full order methodology for the solution of 3D magneto‐mechanical problems with application to magnetic resonance imaging scanners

Parametric reduced order models based on a Riemannian barycentric interpolation

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