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.
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.
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, conducting uncertainty quantification analyses is fundamental to improve the predictive capabilities of the numerical simulations. For largescale, 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, forward model 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. It also enables efficient computation of sensitivity analyses which highlight that epistemic uncertainty plays an important role in the solution of irradiated, particle-laden turbulent flow.
This report documents the results of an FY22 ASC V&V level 2 milestone demonstrating new algorithms for multifidelity uncertainty quantification. Part I of the report describes the algorithms, studies their performance on a simple model problem, and then deploys the methods to a thermal battery example from the open literature. Part II (restricted distribution) applies the multifidelity UQ methods to specific thermal batteries of interest to the NNSA/ASC program.
Communication networks have evolved to a level of sophistication that requires computer models and numerical simulations to understand and predict their behavior. A network simulator is a software that enables the network designer to model several components of a computer network such as nodes, routers, switches and links and events such as data transmissions and packet errors in order to obtain device and network level metrics. Network simulations, as many other numerical approximations that model complex systems, are subject to the specification of parameters and operative conditions of the system. Very often the full characterization of the system and their input is not possible, therefore Uncertainty Quantification (UQ) strategies need to be deployed to evaluate the statistics of its response and behavior. UQ techniques, despite the advancements in the last two decades, still suffer in the presence of a large number of uncertain variables and when the regularity of the systems response cannot be guaranteed. In this context, multifidelity approaches have gained popularity in the UQ community recently due to their flexibility and robustness with respect to these challenges. The main idea behind these techniques is to extract information from a limited number of high-fidelity model realizations and complement them with a much larger number of a set of lower fidelity evaluations. The final result is an estimator with a much lower variance, i.e. a more accurate and reliable estimator can be obtained. In this contribution we investigate the possibility to deploy multifidelity UQ strategies to computer network analysis. Two numerical configurations are studied based on a simplified network with one client and one server. Preliminary results for these tests suggest that multifidelity sampling techniques might be used as effective tools for UQ tools in network applications.
Network modeling is a powerful tool to enable rapid analysis of complex systems that can be challenging to study directly using physical testing. Two approaches are considered: emulation and simulation. The former runs real software on virtualized hardware, while the latter mimics the behavior of network components and their interactions in software. Although emulation provides an accurate representation of physical networks, this approach alone cannot guarantee the characterization of the system under realistic operative conditions. Operative conditions for physical networks are often characterized by intrinsic variability (payload size, packet latency, etc.) or a lack of precise knowledge regarding the network configuration (bandwidth, delays, etc.); therefore uncertainty quantification (UQ) strategies should be also employed. UQ strategies require multiple evaluations of the system with a number of evaluation instances that roughly increases with the problem dimensionality, i.e., the number of uncertain parameters. It follows that a typical UQ workflow for network modeling based on emulation can easily become unattainable due to its prohibitive computational cost. In this paper, a multifidelity sampling approach is discussed and applied to network modeling problems. The main idea is to optimally fuse information coming from simulations, which are a low-fidelity version of the emulation problem of interest, in order to decrease the estimator variance. By reducing the estimator variance in a sampling approach it is usually possible to obtain more reliable statistics and therefore a more reliable system characterization. Several network problems of increasing difficulty are presented. For each of them, the performance of the multifidelity estimator is compared with respect to the single fidelity counterpart, namely, Monte Carlo sampling. For all the test problems studied in this work, the multifidelity estimator demonstrated an increased efficiency with respect to MC.
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 uncertainparameters involvedandthe high computational costofflow simulations. These difficulties are addressedin this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying themin the current studyto large-eddy simulations ofajet incrossflow 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 system's 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.
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 system’s 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. Finally, 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.