A decomposition‐based approach to uncertainty analysis of feed‐forward multicomponent systems

Amaral, Sergio; Allaire, Douglas; Willcox, Karen

doi:10.1002/nme.4779

Cited by 41 publications

(41 citation statements)

References 35 publications

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“…Our proof follows the standard importance sampling convergence analysis techniques [4,52]. From (4.6)-(4.7),…”

Section: Theorem 42 If the Dd-convergence Condition Is Satisfied Fomentioning

confidence: 93%

“…We introduce a domain-decomposed uncertainty analysis approach based on the methodology of importance sampling [51,52], which can be decomposed into two stages: offline (initial sampling) and online (reweighting) [4]. The offline stage of our method carries out Monte Carlo simulation at the local subdomain level.…”

Section: Dduq Algorithmmentioning

confidence: 99%

“…In this paper, we build upon the distributed method for forward propagation of uncertainty introduced by Amaral, Allaire, and Willcox [4]. We develop a mathematical framework using iterative domain decomposition.…”

mentioning

confidence: 99%

“…(See [4] for a detailed discussion of other density estimation methods.) In the following, the estimated target input PDF is denoted byπ ξi,τi (ξ i , τ i ).…”

mentioning

confidence: 99%

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A Domain Decomposition Approach for Uncertainty Analysis

Liao¹,

Willcox²

2015

SIAM J. Sci. Comput.

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Abstract. This paper proposes a decomposition approach for uncertainty analysis of systems governed by partial differential equations (PDEs). The system is split into local components using domain decomposition. Our domain-decomposed uncertainty quantification (DDUQ) approach performs uncertainty analysis independently on each local component in an "offline" phase, and then assembles global uncertainty analysis results using precomputed local information in an "online" phase. At the heart of the DDUQ approach is importance sampling, which weights the precomputed local PDE solutions appropriately so as to satisfy the domain decomposition coupling conditions. To avoid global PDE solves in the online phase, a proper orthogonal decomposition reduced model provides an efficient approximate representation of the coupling functions. 1. Introduction. Many problems arising in computational science and engineering are described by mathematical models of high complexity-involving multiple disciplines, characterized by a large number of parameters, and impacted by multiple sources of uncertainty. Decomposition of a system into subsystems or component parts has been one strategy to manage this complexity. For example, modern engineered systems are typically designed by multiple groups, usually decomposed along disciplinary or subsystem lines, sometimes spanning different organizations and even different geographical locations. Mathematical strategies have been developed for decomposing a simulation task (e.g., domain decomposition methods [45]), for decomposing an optimization task (e.g., domain decomposition for optimal design or control [28,10,29,5]), and for decomposing a complex design task (e.g., decomposition approaches to multidisciplinary optimization [15,34,55]). In this paper we propose a decomposition approach for uncertainty quantification (UQ). In particular, we focus on the simulation of systems governed by stochastic partial differential equations (PDEs) and a domain decomposition approach to quantification of uncertainty in the corresponding quantities of interest.In the design setting, decomposition approaches are not typically aimed at improving computational efficiency, although in some cases decomposition can admit parallelism that would otherwise be impossible [57]. Rather, decomposition is typically employed in situations for which it is infeasible or impractical to achieve tight coupling among the system subcomponents. This inability to achieve tight coupling becomes a particular problem when the goal is to wrap an outer loop (e.g., optimization) around the simulation. In the field of multidisciplinary design optimization (MDO), decomposition is achieved through mathematical formulations such as col-

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“…Our proof follows the standard importance sampling convergence analysis techniques [4,52]. From (4.6)-(4.7),…”

Section: Theorem 42 If the Dd-convergence Condition Is Satisfied Fomentioning

confidence: 93%

Section: Dduq Algorithmmentioning

confidence: 99%

mentioning

confidence: 99%

“…(See [4] for a detailed discussion of other density estimation methods.) In the following, the estimated target input PDF is denoted byπ ξi,τi (ξ i , τ i ).…”

mentioning

confidence: 99%

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A Domain Decomposition Approach for Uncertainty Analysis

Liao¹,

Willcox²

2015

SIAM J. Sci. Comput.

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“…Feed-forward coupling is usually easier to deal with; it has been tackled using approximations such as surrogates 11 and decomposition combined with recomposition through importance sampling. 12 Here, we focus on the more complicated case of a feedback-coupled system. We treat all disciplinary analyses as black-boxes (i.e., they can be viewed in terms of their inputs and outputs, and knowledge of their internal mechanisms is not needed) and we develop a non-intrusive approach that does not modify the disciplinary analysis.…”

Section: Introductionmentioning

confidence: 99%

Multifidelity Uncertainty Propagation in Coupled Multidisciplinary Systems

Chaudhuri

Willcox

2016

18th AIAA Non-Deterministic Approaches Conference

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Fixed point iteration is a common strategy to handle interdisciplinary coupling within a coupled multidisciplinary analysis. For each coupled analysis, this requires a large number of disciplinary high-fidelity simulations to resolve the interactions between different disciplines. When embedded within an uncertainty analysis loop (e.g., with Monte Carlo sampling over uncertain parameters) the number of high-fidelity disciplinary simulations quickly becomes prohibitive, since each sample requires a fixed point iteration and the uncertainty analysis typically involves thousands or even millions of samples. This paper develops a method for uncertainty analysis in feedback-coupled black-box systems that leverages adaptive surrogates to reduce the number of cases for which fixed point iteration is needed. The multifidelity coupled uncertainty propagation method is an iterative process that uses surrogates for approximating the coupling variables and adaptive sampling strategies to refine the surrogates. The adaptive sampling strategies explored in this work are residual error, information gain, and weighted information gain. The surrogate models are adapted in a way that does not compromise accuracy of the uncertainty analysis relative to the original coupled high-fidelity problem.

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Adaptive experimental design for multi‐fidelity surrogate modeling of multi‐disciplinary systems

Jakeman

Friedman

Eldred

et al. 2022

Numerical Meth Engineering

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We present an adaptive algorithm for constructing surrogate models of multi-disciplinary systems composed of a set of coupled components. With this goal we introduce "coupling" variables with a priori unknown distributions that allow surrogates of each component to be built independently. Once built, the surrogates of the components are combined to form an integrated-surrogate that can be used to predict system-level quantities of interest at a fraction of the cost of the original model. The error in the integrated-surrogate is greedily minimized using an experimental design procedure that allocates the amount of training data, used to construct each component-surrogate, based on the contribution of those surrogates to the error of the integrated-surrogate. The multi-fidelity procedure presented is a generalization of multi-index stochastic collocation that can leverage ensembles of models of varying cost and accuracy, for one or more components, to reduce the computational cost of constructing the integrated-surrogate. Extensive numerical results demonstrate that, for a fixed computational budget, our algorithm is able to produce surrogates that are orders of magnitude more accurate than methods that treat the integrated system as a black-box.

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A decomposition‐based approach to uncertainty analysis of feed‐forward multicomponent systems

Cited by 41 publications

References 35 publications

A Domain Decomposition Approach for Uncertainty Analysis

A Domain Decomposition Approach for Uncertainty Analysis

Multifidelity Uncertainty Propagation in Coupled Multidisciplinary Systems

Adaptive experimental design for multi‐fidelity surrogate modeling of multi‐disciplinary systems

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