Formulations for Surrogate-Based Optimization with Data Fit, Multifidelity, and Reduced-Order Models

Eldred, Michael; Dunlavy, Daniel M.

doi:10.2514/6.2006-7117

Cited by 95 publications

(68 citation statements)

References 29 publications

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“…The paper [84] categorizes surrogate models into three different classes: data-fit models, projection-based reduced models, and hierarchical models. Data-fit models include response surface methods that use interpolation or regression of simulation data to fit a model for the system output as a function of the parameters.…”

Section: Parametric Model Reduction and Surrogate Modelingmentioning

confidence: 99%

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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Abstract. Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for which the equations governing the system behavior depend on a set of parameters. Examples include parameterized partial differential equations and large-scale systems of parameterized ordinary differential equations. The goal of parametric model reduction is to generate low-cost but accurate models that characterize system response for different values of the parameters. This paper surveys state-of-the-art methods in projection-based parametric model reduction, describing the different approaches within each class of methods for handling parametric variation and providing a comparative discussion that lends insights to potential advantages and disadvantages in applying each of the methods. We highlight the important role played by parametric model reduction in design, control, optimization, and uncertainty quantification-settings that require repeated model evaluations over different parameter values.

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Section: Parametric Model Reduction and Surrogate Modelingmentioning

confidence: 99%

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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“…[26], second-order Taylor series approximations are investigated. In both cases, a trust-region model management framework [28] is used to adaptively manage the extent of the approximations and ensure convergence of the OUU process. Surrogate models are used for both the objective and the constraint functions, although the use of surrogates is only required for the functions containing statistical results; deterministic functions may remain explicit is desired.…”

Section: Sequential/surrogate-based Sebdomentioning

confidence: 99%

DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis.

Eldred

Vigil

Dalbey

et al. 2011

Self Cite

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The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers.This report serves as a theoretical manual for selected algorithms implemented within the DAKOTA software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of DAKOTA-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of DAKOTA's iterative analysis capabilities.4

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“…Moreover, the suggested FOA can treat only the rigidity of the body structure. On the other hand, some researches have also been tried to construct the low-fidelity CAE models to reduce the computational cost for the optimization of the complicate structural design of high-fidelity models (6), (7) . However, it is difficult to establish a unified theory and manner to construct low-fidelity models for the complicate 3D-bodies.…”

Section: Introductionmentioning

confidence: 99%

Simplified Deformation Analysis of 3D-body by First Order Analysis

Khan

Yamazaki

Oda

et al. 2007

JAMDSM

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This paper proposes a simplified analysis model of complex solid structure for three-dimensional bodies (3D-bodies) in the First Order Analysis (FOA). A simplified finite element composed of the beam elements is suggested for the deformation analysis of 3D-bodies by extending concept of conforming beam element for the finite element method (FEM). When a complex solid structure is simplified to an assemblage of simple elements applied element forces such as axial forces, shear forces, bending moments as well as twisting moments, the total stiffness equation for the FOA of the solid structure is constructed approximately and solved for the given boundary and loading conditions by the usual manner of the FEM. Then, the total deformation of the complex structure is estimated by the simplified model and the element forces are calculated in the element level. It is found that the finite element analysis via developed simplified element analysis can estimate deformations of complex 3D-bodies in a rational precision, and the results of the analysis are useful for considering the load transmitting path of the structure and for designing a better structure by changing the stiffness of structural components.

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Formulations for Surrogate-Based Optimization with Data Fit, Multifidelity, and Reduced-Order Models

Cited by 95 publications

References 29 publications

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis.

Simplified Deformation Analysis of 3D-body by First Order Analysis

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