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

Geraci, Gianluca; Eldred, Michael; Iaccarino, Gianluca

doi:10.2514/6.2017-1951

Cited by 48 publications

(60 citation statements)

References 17 publications

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“…The AMISC approximations, however, achieve the same level of error as the single fidelity approach at only a fraction of the work. The results in Figure 9 are generated by setting = 1 in (29). Despite the fact we only adapt to reduce the error in the mean, we still can reduce the ∞ error in the AMISC and single-fidelity approximations.…”

Section: Advection Diffusion Modelmentioning

confidence: 99%

“…Multi-level/multi-index surrogate methods are closely related to many multilevel/multifidelity sampling algorithms. 24,25,[28][29][30][31][32] These sampling algorithms leverage correlation between the outputs of multiple models to reduce the variance in statistical estimators of quantities such as expectation. This variance reduction can result in orders of magnitude reduction in the computational cost of quantifying uncertainty, but like traditional MC sampling, the error decreases slowly as the number of samples is increased which can still render this approach infeasible in some contexts.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive multi‐index collocation for uncertainty quantification and sensitivity analysis

Jakeman

Eldred

Geraci

et al. 2019

Numerical Meth Engineering

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Summary In this paper, we present an adaptive algorithm to construct response surface approximations of high‐fidelity models using a hierarchy of lower fidelity models. Our algorithm is based on multi‐index stochastic collocation and automatically balances physical discretization error and response surface error to construct an approximation of model outputs. This surrogate can be used for uncertainty quantification (UQ) and sensitivity analysis (SA) at a fraction of the cost of a purely high‐fidelity approach. We demonstrate the effectiveness of our algorithm on a canonical test problem from the UQ literature and a complex multiphysics model that simulates the performance of an integrated nozzle for an unmanned aerospace vehicle. We find that, when the input‐output response is sufficiently smooth, our algorithm produces approximations that can be over two orders of magnitude more accurate than single fidelity approximations for a fixed computational budget.

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Section: Advection Diffusion Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive multi‐index collocation for uncertainty quantification and sensitivity analysis

Jakeman

Eldred

Geraci

et al. 2019

Numerical Meth Engineering

Self Cite

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“…MLMF schemes can be implemented for either the same or different numbers of high-fidelity and low-fidelity model levels. For further details, the reader is referred to [47].…”

Section: A Multilevel-multifidelity Approachmentioning

confidence: 99%

“…Intuitively this is correct since for an increase in correlation and/or in the cost ratio, more low-fidelity simulations (i.e., larger r ) are required. To ensure our model correlations are sufficiently high for all fidelity and discretization levels, we employ the version of the MLMF algorithm detailed in [47].…”

Section: A Multilevel-multifidelity Approachmentioning

confidence: 99%

“…The formulae for the optimal Outlet Flow Model TAWSS MC MLMC MLMF MLMF MC MLMC MLMF MLMF 3D-1D 3D-1D-0D 3D-1D 3D-1D- number of samples needed for extrapolation are given by (13), (18), and (20) for the MLMC, MFMC, and MLMF estimators, respectively. These formulae have been used successfully for applications such as engine nozzles, scramjets, and wind turbines [47,69]. To validate these for cardiovascular modeling, we needed to ensure that the cost of converging to various target estimator variances is reflective of the projected extrapolated costs.…”

Section: Extrapolated Cost Validationmentioning

confidence: 99%

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Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics

Fleeter

Geraci

Schiavazzi

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an efficient uncertainty quantification framework utilizing a multilevel multifidelity Monte Carlo (MLMF) estimator to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. This is achieved by leveraging three cardiovascular model fidelities, each with varying spatial resolution to rigorously quantify the variability in hemodynamic outputs. We derive two low-fidelity models (zero-and one-dimensional) that we use to obtain different estimators. Our goal is to investigate and compare the efficiency of estimators built from these two low-fidelity model alternatives and our high-fidelity three-dimensional models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. Our goal is to demonstrate that for this application it is possible to accelerate the convergence of the estimators by utilizing a MLMF paradigm. Therefore, we compare our approach to single fidelity Monte Carlo estimators and to a multilevel Monte Carlo approach based only on three-dimensional simulations, but leveraging multiple spatial resolutions. We demonstrate significant, on the order of 10 to 100 times, reduction in total computational cost with the MLMF estimators. We also examine the differing properties of the MLMF estimators in healthy versus diseased models, as well as global versus local quantities of interest. As expected, global quantities such as outlet pressure and flow show larger reductions than local quantities, such as those relating to wall shear stress, as the latter rely more heavily on the highest fidelity model evaluations. Similarly, healthy models show larger reductions than diseased models. In all cases, our workflow coupling Dakota's MLMF estimators with the SimVascular cardiovascular workflow make uncertainty quantification feasible for constrained computational budgets. range of diseases and anatomies. Coronary artery disease is the most prevalent cause of death in the United States [4], and has thus been the subject of many modeling studies. These include computing fractional flow reserve for patients with coronary stenoses [5] and assessing differences in the hemodynamic and mechanical response of arterial and venous grafts towards determining cause of vein graft failure [6]. Computational models have also been applied to congenital heart disease for prognosis and treatment planning, from testing designs for surgical interventions of single ventricle congenital heart disease [7-9] to thrombotic risk assessment for Kawasaki disease [10][11][12], and assessment of disease progression and mechanical stimuli in pulmonary hypertension [13,14]. Hemodynamic studies are also used for additional disease cases, such as analyzing bloo...

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Adaptive multi‐index collocation for uncertainty quantification and sensitivity analysis

Jakeman¹,

Eldred²,

Geraci³

et al. 2020

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

In this paper, we present an adaptive algorithm to construct response surface approximations of high-fidelity models using a hierarchy of lower fidelity models. Our algorithm is based on multi-index stochastic collocation and automatically balances physical discretization error and response surface error to construct an approximation of model outputs. This surrogate can be used for uncertainty quantification (UQ) and sensitivity analysis (SA) at a fraction of the cost of a purely high-fidelity approach. We demonstrate the effectiveness of our algorithm on a canonical test problem from the UQ literature and a complex multiphysics model that simulates the performance of an integrated nozzle for an unmanned aerospace vehicle. We find that, when the input-output response is sufficiently smooth, our algorithm produces approximations that can be over two orders of magnitude more accurate than single fidelity approximations for a fixed computational budget.

show abstract

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

Cited by 48 publications

References 17 publications

Adaptive multi‐index collocation for uncertainty quantification and sensitivity analysis

Adaptive multi‐index collocation for uncertainty quantification and sensitivity analysis

Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics

Adaptive multi‐index collocation for uncertainty quantification and sensitivity analysis

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