Begell House Inc.
International Journal for Uncertainty Quantification
IJUQ
2152-5080
6
6
2016
EMPIRICAL EVALUATION OF BAYESIAN OPTIMIZATION IN PARAMETRIC TUNING OF CHAOTIC SYSTEMS
467-485
Mudassar
Abbas
Department of Computer Science, School of Science, Aalto University, Espoo, Finland
Alexander
Ilin
Department of Computer Science, School of Science, Aalto University, Espoo, Finland
Antti
Solonen
Lappeenranta University of Technology, Laboratory of Applied Mathematics
Janne
Hakkarainen
Finnish Meterological Institute, Helsinki, Finland
Erkki
Oja
Department of Computer Science, School of Science, Aalto University, Espoo, Finland
Heikki
Jarvinen
University of Helsinki, Helsinki, Finland
In this work, we consider the Bayesian optimization (BO) approach for parametric tuning of complex chaotic systems. Such problems arise, for instance, in tuning the sub-grid-scale parameterizations in weather and climate models. For such problems, the tuning procedure is generally based on a performance metric which measures how well the tuned model fits the data. This tuning is often a computationally expensive task. We show that BO, as a tool for finding the extrema of computationally expensive objective functions, is suitable for such tuning tasks. In the experiments, we consider tuning parameters of two systems: a simplified atmospheric model and a low-dimensional chaotic system. We show that BO is able to tune parameters of both the systems with a low number of objective function evaluations.
A CROSS-ENTROPY METHOD ACCELERATED DERIVATIVE-FREE RBDO ALGORITHM
487-500
Tian
Gao
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
Jinglai
Li
University of Liverpool, Institute of Natural Sciences and School of
Mathematical Sciences
Shanghai Jiaotong University
Shanghai 200240, China
Many engineering applications require optimization of the system performance subject to reliability constraints, which are commonly referred to as the reliability based design and optimization (RBDO) problems. In this work we propose a derivative-free algorithm to solve the RBDO problems. In particular, we focus on the type of RBDO problems where the objective function is deterministic and easy to evaluate, whereas the reliability constraints involve very small failure probabilities. The algorithm consists of solving a set of subproblems, in which simple surrogate models of the reliability constraints are constructed and used in solving the subproblems. Moreover, we employ a cross-entropy (CE) method with sample reweighting to evaluate the rare failure probabilities, which constructs the surrogate for the reliability constraints by performing only a single full CE simulation in each iteration. Finally we demonstrate the performance of the proposed method with both academic and practical examples.
FORWARD AND INVERSE UNCERTAINTY QUANTIFICATION USING MULTILEVEL MONTE CARLO ALGORITHMS FOR AN ELLIPTIC NONLOCAL EQUATION
501-514
Ajay
Jasra
Department of Statistics & Applied Probability National University of Singapore, Singapore
Kody J. H.
Law
School of Mathematics, University of Manchester, Manchester, UK, M13 9PL
Yan
Zhou
Department of Statistics & Applied Probability National University of Singapore, Singapore
This paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a probability measure. It is shown that the induced probability measure on some quantities of interest arising from functionals of the solution to the equation with random inputs is well-defined,s as is the posterior distribution on parameters given observations. As the elliptic nonlocal equation cannot be solved approximate posteriors are constructed. The multilevel Monte Carlo (MLMC) and multilevel sequential Monte Carlo (MLSMC) sampling algorithms are used for a priori and a posteriori estimation, respectively, of quantities of interest. These algorithms reduce the amount of work to estimate posterior expectations, for a given level of error, relative to Monte Carlo and i.i.d. sampling from the posterior at a given level of approximation of the solution of the elliptic nonlocal equation.
A NEW INVERSE METHOD FOR THE UNCERTAINTY QUANTIFICATION OF SPATIALLY VARYING RANDOM MATERIAL PROPERTIES
515-531
Gun Jin
Yun
Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul, South Korea, 08826
Shen
Shang
AZZ IWSI 2225 Skyland Court Norcross, Georgia 30071, USA
In this paper, a new inverse uncertainty quantification method was proposed to identify statistical parameters associated with spatially varying material properties and to reconstruct their heterogeneous distributions from limited experimental measurements. The proposed method parameterizes statistical models of random fields with analytic co-variance functions and spectral decomposition into Karhunen-Loeve random variables. The statistical model parameters are identified by an experimental-numerical inverse analysis method, which is expected to significantly reduce time and cost required for quantification of material uncertainties.
SCENARIO DISCOVERY WORKFLOW FOR ROBUST PETROLEUM RESERVOIR DEVELOPMENT UNDER UNCERTAINTY
533-559
Rui
Jiang
Stanford University
Dave
Stern
ExxonMobil Upstream Research Co., 22777 Springwoods Village Parkway, Spring, Texas 77389, USA
Thomas C.
Halsey
ExxonMobil Upstream Research Co., 22777 Springwoods Village Parkway, Spring, Texas 77389, USA
Tom
Manzocchi
UCD School of Geological Sciences, University College Dublin, Dublin 4, Ireland
Subsurface uncertainty creates large economic risks for the development of hydrocarbon reservoirs, driving the need for a decision-making procedure that is robust with respect to this uncertainty. In current practice, decisions are often made based on a single geologic scenario, and uncertainty is modeled in terms of parametric variations around best-estimate values within that scenario. In such a procedure, the impact of other possible geological scenarios upon the performance of a development plan is not explicitly evaluated. To improve decision making, reservoir models with different geological concepts (e.g., different environments of deposition) should be built to capture the full range of uncertainty. However, it is difficult to analyze the results from many models and provide summary information pertinent to business needs. In this paper, a scenario discovery-based outcome analysis workflow is described to systematically explore the result of many (50 to 10,000 or more) reservoir simulation runs. The workflow includes defining performance metrics to reflect business needs, exploring and defining outcome scenarios, searching for relationships between geological parameters and outcomes, and selecting and investigating individual representative cases. Supported by various data mining and data visualization techniques, this workflow may help decision-makers to better understand the potential business impacts of the uncertainty and develop insights concerning geological parameters that control these impacts. We present two examples of this workflow based on a subset of the SAIGUP [Manzocchi et al., Petrol. Geosci., 141(1):3−15, 2008] dataset containing 2268 reservoir simulation models, from a full factorial combination of four sedimentology parameters and three structural parameters. In the first example, we examine the shape of production profiles, demonstrating the identification of geological origins for different shapes of production curves using only a small fraction of the full factorial simulation set. In the second example, we analyze the factors influencing water breakthrough time. For both examples, we identify representative reservoir models to ground decision-making in concrete instances.
INDEX VOLUME 6, 2016
561-565