Sequential Design for Gaussian Process Surrogates in Noisy Level Set Estimation

We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels and sequential design frameworks. Our focus is on strongly stochastic samplers, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. We introduce the use of four GP-based metamodels in level set estimation that are robust to noise misspecification, and evaluate the performance of them. In conjunction with these metamodels, we develop several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions for the proposed metamodels. To expedite sequential design in stochastic experiments, we also develop adaptive batching designs, which are natural extensions of sequential design heuristics with the benefit of replication growing as response features are learned, inputs concentrate, and the metamodeling overhead rises. We develop four novel schemes that simultaneously or sequentially determine the sequential design inputs and the respective number of replicates. Our schemes are benchmarked by using synthetic examples and an application in quantitative finance (Bermudan option pricing)

Improvement of code behaviour in a design of experiments by metamodeling

It is now common practice in nuclear engineering to base extensive studies on numerical computer models. These studies require to run computer codes in potentially thousands of numerical configurations and without expert individual controls on the computational and physical aspects of each simulations.In this paper, we compare different statistical metamodeling techniques and show how metamodels can help to improve the global behaviour of codes in these extensive studies. We consider the metamodeling of the Germinal thermalmechanical code by Kriging, kernel regression and neural networks. Kriging provides the most accurate predictions while neural networks yield the fastest metamodel functions. All three metamodels can conveniently detect strong computation failures. It is however significantly more challenging to detect code instabilities, that is groups of computations that are all valid, but numerically inconsistent with one another. For code instability detection, we find that Kriging provides the most useful tools

Development of reduced polynomial chaos-Kriging metamodel for uncertainty quantification of computational aerodynamics

2018 Summer.Includes bibliographical references.Computational fluid dynamics (CFD) simulations are a critical component of the design and development of aerodynamic bodies. However, as engineers attempt to capture more detailed physics, the computational cost of simulations increases. This limits the ability of engineers to use robust or multidisciplinary design methodologies for practical engineering applications because the computational model is too expensive to evaluate for uncertainty quantification studies and off-design performance analysis. Metamodels (surrogate models) are a closed-form mathematical solution fit to only a few simulation responses which can be used to remedy this situation by estimating off-design performance and stochastic responses of the CFD simulation for far less computational cost. The development of a reduced polynomial chaos-Kriging (RPC-K) metamodel is another step towards eliminating simulation gridlock by capturing the relevant physics of the problem in a cheap-to-evaluate metamodel using fewer CFD simulations. The RPC-K metamodel is superior to existing technologies because its model reduction methodology eliminates the design parameters which contribute little variance to the problem before fitting a high-fidelity metamodel to the remaining data. This metamodel can capture non-linear physics due to its inclusion of both the long-range trend information of a polynomial chaos expansion and local variations in the simulation data through Kriging. In this thesis, the RPC-K metamodel is developed, validated on a convection-diffusion-reaction problem, and applied to the NACA 4412 airfoil and aircraft engine nacelle problems. This research demonstrates the metamodel's effectiveness over existing polynomial chaos and Kriging metamodels for aerodynamics applications because of its ability to fit non-linear fluid flows with far fewer CFD simulations. This research will allow aerospace engineers to more effectively take advantage of detailed CFD simulations in the development of next-generation aerodynamic bodies through the use of the RPC-K metamodel to save computational cost

Primary Healthcare Delivery Network Simulation using Stochastic Metamodels

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this recordA discrete-event simulation (DES) of the network of primary health centers (PHCs) in a region can be used to evaluate the effect of changes in patient flow on operational outcomes across the network, and can also form the base simulation to which simulations of secondary and tertiary care facilities can be added. We present a DES of a network of PHCs using stochastic metamodels developed from more detailed DES models of PHCs (‘parent’ simulations), which were developed separately for comprehensively analyzing individual PHC operations. The stochastic metamodels are DESs in their own right. They are simplified versions of the parent simulation with full-featured representations of only those components relevant to the analysis at hand. We show that the outputs of interest from the metamodels and the parent simulations (including the network simulations) are statistically similar and that our metamodel-based network simulation yields reductions of up to 80% in runtimes

Design and analysis of computer experiments for stochastic systems

Ph.DDOCTOR OF PHILOSOPH