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Multifidelity uncertainty quantification using spectral stochastic discrepancy models

Handbook of Uncertainty Quantification

Eldred, Michael S.; Ng, Leo W.T.; Barone, Matthew F.; Domino, Stefan P.

When faced with a restrictive evaluation budget that is typical of today's highfidelity simulation models, the effective exploitation of lower-fidelity alternatives within the uncertainty quantification (UQ) process becomes critically important. Herein, we explore the use of multifidelity modeling within UQ, for which we rigorously combine information from multiple simulation-based models within a hierarchy of fidelity, in seeking accurate high-fidelity statistics at lower computational cost. Motivated by correction functions that enable the provable convergence of a multifidelity optimization approach to an optimal high-fidelity point solution, we extend these ideas to discrepancy modeling within a stochastic domain and seek convergence of a multifidelity uncertainty quantification process to globally integrated high-fidelity statistics. For constructing stochastic models of both the low-fidelity model and the model discrepancy, we employ stochastic expansion methods (non-intrusive polynomial chaos and stochastic collocation) computed by integration/interpolation on structured sparse grids or regularized regression on unstructured grids. We seek to employ a coarsely resolved grid for the discrepancy in combination with a more finely resolved Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. Grid for the low-fidelity model. The resolutions of these grids may be defined statically or determined through uniform and adaptive refinement processes. Adaptive refinement is particularly attractive, as it has the ability to preferentially target stochastic regions where the model discrepancy becomes more complex, i.e., where the predictive capabilities of the low-fidelity model start to break down and greater reliance on the high-fidelity model (via the discrepancy) is necessary. These adaptive refinement processes can either be performed separately for the different grids or within a coordinated multifidelity algorithm. In particular, we present an adaptive greedy multifidelity approach in which we extend the generalized sparse grid concept to consider candidate index set refinements drawn from multiple sparse grids, as governed by induced changes in the statistical quantities of interest and normalized by relative computational cost. Through a series of numerical experiments using statically defined sparse grids, adaptive multifidelity sparse grids, and multifidelity compressed sensing, we demonstrate that the multifidelity UQ process converges more rapidly than a single-fidelity UQ in cases where the variance of the discrepancy is reduced relative to the variance of the high-fidelity model (resulting in reductions in initial stochastic error), where the spectrum of the expansion coefficients of the model discrepancy decays more rapidly than that of the high-fidelity model (resulting in accelerated convergence rates), and/or where the discrepancy is more sparse than the high-fidelity model (requiring the recovery of fewer significant terms).

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TYPE Book YEAR 2017
OSTIScopus

Multilevel-multifidelity acceleration of PDE-constrained optimization

58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2017

Monschke, Jason A.; Eldred, Michael S.

Many engineering design problems can be formulated in the framework of partial differential equation (PDE) constrained optimization. The discretization of a PDE leads to multiple levels of resolution with varying degrees of numerical solution accuracy. Coarse discretizations require less computational time at the expense of increased error. Often there are also reduced fidelity models available, with simplifications to the physics models that are computationally easier to solve. This research develops an up to second-order consistent multilevel-multifidelity (MLMF) optimization scheme that exploits the reduced cost resulting from coarse discretization and reduced fidelity to more efficiently converge to the optimum of a fine-grid high-fidelity problem. This scheme distinguishes multilevel approaches applied to discretizations from multifidelity approaches applied to model forms, and navigates both hierarchies to accelerate convergence. Additive, multiplicative, or a combination of both corrections can be applied to the sub-problems to enforce up to second-order consistency with the fine-grid high-fidelity results. The MLMF optimization algorithm is a wrapper around a subproblem optimization solver, and the MLMF scheme is provably convergent if the subproblem optimizer is provably convergent. Heuristics are developed for efficiently tuning optimization tolerances and iterations at each level and fidelity based on relative solution cost. Accelerated convergence is demonstrated for a simple one-dimensional problem and aerodynamic shape optimization of a transonic airfoil.

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TYPE Conference Poster YEAR 2017
DOIOSTIScopusDOIOSTIScopus

Global sensitivity analysis and quantification of model error for large eddy simulation in scramjet design

19th AIAA Non-Deterministic Approaches Conference, 2017

Huan, Xun H.; Safta, Cosmin S.; Sargsyan, Khachik S.; Geraci, Gianluca G.; Eldred, Michael S.; Vane, Zachary P.; Lacaze, Guilhem M.; Oefelein, Joseph C.; Najm, H.N.

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress towards optimal engine designs requires both accurate flow simulations as well as uncertainty quantification (UQ). However, performing UQ for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. We address these difficulties by combining UQ algorithms and numerical methods to the large eddy simulation of the HIFiRE scramjet configuration. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, helping reduce the stochastic dimension of the problem and discover sparse representations. Second, as models of different fidelity are available and inevitably used in the overall UQ assessment, a framework for quantifying and propagating the uncertainty due to model error is introduced. These methods are demonstrated on a non-reacting scramjet unit problem with parameter space up to 24 dimensions, using 2D and 3D geometries with static and dynamic treatments of the turbulence subgrid model.

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TYPE Conference Poster YEAR 2017
DOIOSTIScopusDOIOSTIScopus
Results 101–125 of 219
Results 101–125 of 219