Gradient-based constrained optimization using a database of linear reduced-order models

Choi, Youngsoo; Boncoraglio, Gabriele; Anderson, Spenser; Amsallem, David; Farhat, Charbel

doi:10.1016/j.jcp.2020.109787

Cited by 71 publications

(52 citation statements)

References 32 publications

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“…Optimization done using greedy methods may take more time than full HDM optimization. In Choi et al, 65 for one of the cases shown, a full HDM optimization took almost 1/50th of the time of the off-line basis building procedure. Adaptive sampling is on-line only: each call on the ROM might entail taking a new snapshot.…”

Section: Samplingmentioning

confidence: 99%

“…This estimator can then be used to address a known problem in greedy methods (mentioned in Paul-Dubois-Taine and Amsallem 64 and Choi et al 65 ) using the residual as error estimators, which is that the residual might not reflect the proper scale of the error. The leave-one-out error estimates error for a region of parameter values, while this proposed method estimates the error for a given set of parameter values.…”

Section: Error Estimation and Controlmentioning

confidence: 99%

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Model order reduction in aerodynamics: Review and applications

Mendonça

Afonso

Lau

2019

Proceedings of the Institution of Mechanical Engineers, Part G:

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The need of the aerospace industry, at national or European level, of faster yet reliable computational fluid dynamics models is the main drive for the application of model reduction techniques. This need is linked to the time cost of high-fidelity models, rendering them inefficient for applications like multi-disciplinary optimization. With the goal of testing and applying model reduction to computational fluid dynamics models applicable to lifting surfaces, a bibliographical research covering reduction of nonlinear, dynamic, or steady models was conducted. This established the prevalence of projection and least mean squares methods, which rely on solutions of the original high-fidelity model and their proper orthogonal decomposition to work. Other complementary techniques such as adaptive sampling, greedy sampling, and hybrid models are also presented and discussed. These projection and least mean squares methods are then tested on simple and documented benchmarks to estimate the error and speed-up of the reduced order models thus generated. Dynamic, steady, nonlinear, and multiparametric problems were reduced, with the simplest version of these methods showing the most promise. These methods were later applied to single parameter problems, namely the lid-driven cavity with incompressible Navier–Stokes equations and varying Reynolds number, and the elliptic airfoil at varying angles of attack for compressible Euler flow. An analysis of the performance of these methods is given at the end of this article, highlighting the computational speed-up obtained with these techniques, and the challenges presented by multiparametric problems and problems showing point singularities in their domain.

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Section: Samplingmentioning

confidence: 99%

Section: Error Estimation and Controlmentioning

confidence: 99%

Model order reduction in aerodynamics: Review and applications

Mendonça

Afonso

Lau

2019

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…where W w ∈ R N f ×n f is a left fluid ROB. Projecting next the overdetermined system (18) onto the subspace represented by the left fluid-structure ROB W q (19) transforms this system into the square counterpart…”

Section: Parametric Pmor For Fsi and Sensitivitiesmentioning

confidence: 99%

“…In  X , interpolate in the AS the computed matrix logarithms j = ( r j ), j = 1, … , N B , entry-by-entry, using weighted sums of radial basis functions applied directly to the parameter points r j , j = 1, … , N B . 19 Let ⋆ = ( r ⋆ ) denote the result of this interpolation. 4.…”

Section: Interpolation In the As On A Matrix Manifoldmentioning

confidence: 99%

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Model Reduction Framework with a New Take on Active Subspaces for Optimization Problems with Linearized Fluid‐Structure Interaction Constraints

Boncoraglio

Farhat

Bou-Mosleh

2020

Numerical Meth Engineering

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In this paper, a new take on the concept of an active subspace for reducing the dimension of the design parameter space in a multidisciplinary analysis and optimization (MDAO) problem is proposed. The new approach is intertwined with the concepts of adaptive parameter sampling, projection-based model order reduction, and a database of linear, projection-based reduced-order models equipped with interpolation on matrix manifolds, in order to construct an efficient computational framework for MDAO. The framework is fully developed for MDAO problems with linearized fluidstructure interaction constraints. It is applied to the aeroelastic tailoring, under flutter constraints, of two different flight systems: a flexible configuration of NASA's Common Research Model; and NASA's Aeroelastic Research Wing #2 (ARW-2). The obtained results illustrate the feasibility of the computational framework for realistic MDAO problems and highlight the benefits of the new approach for constructing an active subspace in both terms of solution optimality and wall-clock time reduction.

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An Augmented Lagrangian Trust‐Region Method With Inexact Gradient Evaluations to Accelerate Constrained Optimization Problems Using Model Hyperreduction

Wen,

Zahr

2024

Numerical Methods in Fluids

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We present an augmented Lagrangian trust‐region method to efficiently solve constrained optimization problems governed by large‐scale nonlinear systems with application to partial differential equation‐constrained optimization. At each major augmented Lagrangian iteration, the expensive optimization subproblem involving the full nonlinear system is replaced by an empirical quadrature‐based hyperreduced model constructed on‐the‐fly. To ensure convergence of these inexact augmented Lagrangian subproblems, we develop a bound‐constrained trust‐region method that allows for inexact gradient evaluations, and specialize it to our specific setting that leverages hyperreduced models. This approach circumvents a traditional training phase because the models are built on‐the‐fly in accordance with the requirements of the trust‐region convergence theory. Two numerical experiments (constrained aerodynamic shape design) demonstrate the convergence and efficiency of the proposed work. A speedup of (for all computational costs, even costs traditionally considered “offline” such as snapshot collection and data compression) relative to a standard optimization approach that does not leverage model reduction is shown.

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Gradient-based constrained optimization using a database of linear reduced-order models

Cited by 71 publications

References 32 publications

Model order reduction in aerodynamics: Review and applications

Model order reduction in aerodynamics: Review and applications

Model Reduction Framework with a New Take on Active Subspaces for Optimization Problems with Linearized Fluid‐Structure Interaction Constraints

An Augmented Lagrangian Trust‐Region Method With Inexact Gradient Evaluations to Accelerate Constrained Optimization Problems Using Model Hyperreduction

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