128 research outputs found
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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)
Constrained multi-objective optimization of process design parameters in settings with scarce data: an application to adhesive bonding
Adhesive joints are increasingly used in industry for a wide variety of
applications because of their favorable characteristics such as high
strength-to-weight ratio, design flexibility, limited stress concentrations,
planar force transfer, good damage tolerance and fatigue resistance. Finding
the optimal process parameters for an adhesive bonding process is challenging:
the optimization is inherently multi-objective (aiming to maximize break
strength while minimizing cost) and constrained (the process should not result
in any visual damage to the materials, and stress tests should not result in
failures that are adhesion-related). Real life physical experiments in the lab
are expensive to perform; traditional evolutionary approaches (such as genetic
algorithms) are then ill-suited to solve the problem, due to the prohibitive
amount of experiments required for evaluation. In this research, we
successfully applied specific machine learning techniques (Gaussian Process
Regression and Logistic Regression) to emulate the objective and constraint
functions based on a limited amount of experimental data. The techniques are
embedded in a Bayesian optimization algorithm, which succeeds in detecting
Pareto-optimal process settings in a highly efficient way (i.e., requiring a
limited number of extra experiments)
Batch Bayesian active learning for feasible region identification by local penalization
Identifying all designs satisfying a set of constraints is an important part of the engineering design process. With physics-based simulation codes, evaluating the constraints becomes considerable expensive. Active learning can provide an elegant approach to efficiently characterize the feasible region, i.e., the set of feasible designs. Although active learning strategies have been proposed for this task, most of them are dealing with adding just one sample per iteration as opposed to selecting multiple samples per iteration, also known as batch active learning. While this is efficient with respect to the amount of information gained per iteration, it neglects available computation resources. We propose a batch Bayesian active learning technique for feasible region identification by assuming that the constraint function is Lipschitz continuous. In addition, we extend current state-of-the-art batch methods to also handle feasible region identification. Experiments show better performance of the proposed method than the extended batch methods
Contextual Optimizer through Neighborhood Estimation for prescriptive analysis
We address the challenges posed by heteroscedastic noise in contextual
decision-making. We propose a consistent Shrinking Neighborhood Estimation
(SNE) technique that successfully estimates contextual performance under
unpredictable variances. Furthermore, we propose a Rate-Efficient Sampling rule
designed to enhance the performance of the SNE. The effectiveness of the
combined solution ``Contextual Optimizer through Neighborhood Estimation"(CONE)
is validated through theorems and numerical benchmarking. The methodologies
have been further deployed to address a staffing challenge in a hospital call
center, exemplifying their substantial impact and practical utility in
real-world scenarios
Sensitivity Prewarping for Local Surrogate Modeling
In the continual effort to improve product quality and decrease operations
costs, computational modeling is increasingly being deployed to determine
feasibility of product designs or configurations. Surrogate modeling of these
computer experiments via local models, which induce sparsity by only
considering short range interactions, can tackle huge analyses of complicated
input-output relationships. However, narrowing focus to local scale means that
global trends must be re-learned over and over again. In this article, we
propose a framework for incorporating information from a global sensitivity
analysis into the surrogate model as an input rotation and rescaling
preprocessing step. We discuss the relationship between several sensitivity
analysis methods based on kernel regression before describing how they give
rise to a transformation of the input variables. Specifically, we perform an
input warping such that the "warped simulator" is equally sensitive to all
input directions, freeing local models to focus on local dynamics. Numerical
experiments on observational data and benchmark test functions, including a
high-dimensional computer simulator from the automotive industry, provide
empirical validation
Design and analysis of computer experiments for stochastic systems
Ph.DDOCTOR OF PHILOSOPH
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