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A generalized approximate control variate framework for multifidelity uncertainty quantification

Journal of Computational Physics

Gorodetsky, Alex A.; Geraci, Gianluca G.; Eldred, Michael S.; Jakeman, John D.

We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost models — which are typically lower fidelity with unknown statistics — are used to reduce the variance in statistical estimators relative to a MC estimator with equivalent cost. We derive the conditions under which our proposed approximate control variate framework recovers existing multifidelity variance reduction schemes as special cases. We demonstrate that existing recursive/nested strategies are suboptimal because they use the additional low-fidelity models only to efficiently estimate the unknown mean of the first low-fidelity model. As a result, they cannot achieve variance reduction beyond that of a control variate estimator that uses a single low-fidelity model with known mean. However, there often exists about an order-of-magnitude gap between the maximum achievable variance reduction using all low-fidelity models and that achieved by a single low-fidelity model with known mean. We show that our proposed approach can exploit this gap to achieve greater variance reduction by using non-recursive sampling schemes. The proposed strategy reduces the total cost of accurately estimating statistics, especially in cases where only low-fidelity simulation models are accessible for additional evaluations. Several analytic examples and an example with a hyperbolic PDE describing elastic wave propagation in heterogeneous media are used to illustrate the main features of the methodology.

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TYPE Journal Article YEAR 2020
ScopusOSTIDOI

A multifidelity multilevel Monte Carlo method for uncertainty propagation in aerospace applications

19th AIAA Non-Deterministic Approaches Conference, 2017

Geraci, Gianluca G.; Eldred, Michael S.; Iaccarino, Gianluca

The accurate evaluation of the performance of complex engineering devices needs to rely on high-fidelity numerical simulations and the systematic characterization and propagation of uncertainties. Several sources of uncertainty may impact the performance of an engineering device through operative conditions, manufacturing tolerances, and even physical models. In the presence of multiphysics systems the number of the uncertain parameters can be fairly large and their propagation through the numerical codes still remains prohibitive because the overall computational budget often allows for only an handful of such high-fidelity realizations. On the other side, common engineering practice can take advantage from a solid history of development and assessment of so called low-fidelity models which albeit less accurate are often capable to at least capture overall trends and parameter dependencies of the system. In this contribution we address the forward propagation of uncertainty parameters relying on statistical estimators built on sequences of numerical and physical discretizations which are provably convergent to the high-fidelity statistics, while exploiting low-fidelity computational models to increase the reliability and confidence in the numerical predictions. The performances of the approaches are presented by means of two fairly complicated aerospace problems, namely the aero-thermo-structural analysis of a turbofan engine nozzle and a flow through a scramjet-like device.

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TYPE Conference Poster YEAR 2017
ScopusOSTI

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

International Journal for Numerical Methods in Engineering

Jakeman, John D.; Friedman, Sam; Eldred, Michael S.; Tamellini, Lorenzo; Gorodetsky, Alex A.; Allaire, Doug

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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TYPE Journal Article YEAR 2022
ScopusOSTIDOI

Adaptive resource allocation for surrogate modeling of systems comprised of multiple disciplines with varying fidelity

Friedman, Sam F.; Jakeman, John D.; Eldred, Michael S.; Tamellini, Lorenzo T.; Gorodestky, Alex G.; Allaire, Doug A.

We present an adaptive algorithm for constructing surrogate models for integrated systems composed of a set of coupled components. With this goal we introduce ‘coupling’ variables with a priori unknown distributions that allow approximations of each component to be built independently. Once built, the surrogates of the components are combined and used to predict system-level quantities of interest (QoI) at a fraction of the cost of interrogating the full system model. We use a greedy experimental design procedure, based upon a modification of Multi-Index Stochastic Collocation (MISC), to minimize the error of the combined surrogate. This is achieved by refining each component surrogate in accordance with its relative contribution to error in the approximation of the system-level QoI. Our adaptation of MISC is a multi-fidelity procedure that can leverage ensembles of models of varying cost and accuracy, for one or more components, to produce estimates of system-level QoI. Several numerical examples demonstrate the efficacy of the proposed approach on systems involving feed-forward and feedback coupling. For a fixed computational budget, the proposed algorithm is able to produce approximations that are orders of magnitude more accurate than approximations that treat the integrated system as a black-box.

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TYPE Other Report YEAR 2021
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Results 1–25 of 185
Results 1–25 of 185