arXiv subjects

Gianluca Geraci

Publications and source records attributed to Gianluca Geraci.

23 records · Page 2Linked to original sources

arXiv2019

Adaptive Multi-index Collocation for Uncertainty Quantification and Sensitivity Analysis

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 multi-physics 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.

math.NA↗

arXiv2019

A Generalized Approximate Control Variate Framework for Multifidelity Uncertainty Quantification

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 multi-model variance reduction schemes as special cases. We demonstrate that these existing strategies use recursive sampling strategies, and as a result, their maximum possible variance reduction is limited to that of a control variate algorithm that uses only a single low-fidelity model with known mean. This theoretical result holds regardless of the number of low-fidelity models and/or samples used to build the estimator. We then derive new sampling strategies within our framework that circumvent this limitation to make efficient use of all available information sources. In particular, we demonstrate that a significant gap can exist, of orders of magnitude in some cases, between the variance reduction achievable by using a single low-fidelity model and our non-recursive approach. We also present initial sample allocation approaches for exploiting this gap. They yield the greatest benefit when augmenting the high-fidelity model evaluations is impractical because, for instance, they arise from a legacy database. 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.

stat.CO↗

arXiv2018

Bi-fidelity approximation for uncertainty quantification and sensitivity analysis of irradiated particle-laden turbulence

Efficiently performing predictive studies of irradiated particle-laden turbulent flows has the potential of providing significant contributions towards better understanding and optimizing, for example, concentrated solar power systems. As there are many uncertainties inherent in such flows, uncertainty quantification is fundamental to improve the predictive capabilities of the numerical simulations. For large-scale, multi-physics problems exhibiting high-dimensional uncertainty, characterizing the stochastic solution presents a significant computational challenge as many methods require a large number of high-fidelity solves. This requirement results in the need for a possibly infeasible number of simulations when a typical converged high-fidelity simulation requires intensive computational resources. To reduce the cost of quantifying high-dimensional uncertainties, we investigate the application of a non-intrusive, bi-fidelity approximation to estimate statistics of quantities of interest associated with an irradiated particle-laden turbulent flow. This method relies on exploiting the low-rank structure of the solution to accelerate the stochastic sampling and approximation processes by means of cheaper-to-run, lower fidelity representations. The application of this bi-fidelity approximation results in accurate estimates of the QoI statistics while requiring a small number of high-fidelity model evaluations.

physics.comp-ph↗

arXiv2018

Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. These difficulties are addressed in this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying them in the current study to large-eddy simulations of a jet in crossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, which can help reduce the systems stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. These methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.

physics.data-an↗

arXiv2018

Multi-fidelity uncertainty quantification of irradiated particle-laden turbulence

The study of complex systems is often based on computationally intensive, high-fidelity, simulations. To build confidence in the prediction accuracy of such simulations, the impact of uncertainties in model inputs on the quantities of interest must be measured. This, however, requires a computational budget that is a possibly large multiple of the cost of a single simulation, and thus may become infeasible for expensive simulation models featuring a large number of uncertain inputs and highly nonlinear behavior. Therefore, this work explores multi-fidelity strategies to accelerate the estimation of the effect of uncertainties. The main idea behind multi-fidelity models is to utilize cheaper, lower-fidelity models - than the intended high-fidelity, expensive model of the problem - to generate a baseline solution that together, with relatively small number of high-fidelity simulations can lead to accurate predictions. The methods are briefly presented, and their performance assessed on an irradiated particle-laden turbulent flow case related to Stanford's PSAAP II particle-based solar energy receiver.

physics.comp-ph↗