Bayesian optimal experimental design for the Shock-tube experiment

Terejanu, Gabriel; Bryant, Corey; Miki, Kenji

doi:10.1088/1742-6596/410/1/012040

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…Over the years, KLD has been used to quantify information gain [62] about the objective function, from a hypothetical experiment (an untried design). The efficacy of the KLD has been extended and demonstrated on various applications including the sensor placement problem [48,28], surrogate modeling [63,9,23], learning missing parameters [60], optimizing an expensive physical response [26], calibrating a physical model [22,29], reliability design [51], efficient design space exploration [38], probabilistic sensitivity analysis [37].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions

Pandita

Bilionis

Panchal

2019

Journal of Mechanical Design

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Bayesian optimal design of experiments (BODE) has been successful in acquiring information about a quantity of interest (QoI) which depends on a black-box function. BODE is characterized by sequentially querying the function at specific designs selected by an infill-sampling criterion. However, most current BODE methods operate in specific contexts like optimization, or learning a universal representation of the black-box function. The objective of this paper is to design a BODE for estimating the statistical expectation of a physical response surface. This QoI is omnipresent in uncertainty propagation and design under uncertainty problems. Our hypothesis is that an optimal BODE should be maximizing the expected information gain in the QoI. We represent the information gain from a hypothetical experiment as the Kullback-Liebler (KL) divergence between the prior and the posterior probability distributions of the QoI. The prior distribution of the QoI is conditioned on the observed data and the posterior distribution of the QoI is conditioned on the observed data and a hypothetical experiment. The main contribution of this paper is the derivation of a semi-analytic mathematical formula for the expected information gain about the statistical expectation of a physical response. The developed BODE is validated on synthetic functions with varying number of input-dimensions. We demonstrate the performance of the methodology on a steel wire manufacturing problem.

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Section: Introductionmentioning

confidence: 99%

Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions

Pandita

Bilionis

Panchal

2019

Journal of Mechanical Design

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“…For example, this idea is used in uncertainty sampling (US) [41] which is a BODE heuristic derived from maximizing the expected information gain about the parameters of the probabilistic surrogate, i.e., the implicit goal of US is to learn the entire response surface. Other examples include the sensor placement problem [48,27,36], surrogate modeling [72,8,24], learning missing parameters [66], optimizing an expensive physical response [26], calibrating a physical model [23,28], reliability design [56], efficient design space exploration [38], probabilistic sensitivity analysis [37], portfolio optimization [21], hyperparameter tuning [71], human experiment design [14], radiation detector placement [46], and estimation of statistical expectation [55].…”

Section: Introductionmentioning

confidence: 99%

Learning Arbitrary Quantities of Interest from Expensive Black-Box Functions through Bayesian Sequential Optimal Design

Pandita,

Awalgaonkar,

Bilionis

et al. 2019

Preprint

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Estimating arbitrary quantities of interest (QoIs) that are non-linear operators of complex, expensive-to-evaluate, black-box functions is a challenging problem due to missing domain knowledge and finite information acquisition budgets. Bayesian optimal design of experiments (BODE) is a family of methods that identify an optimal design of experiments (DOE) under different contexts, such as learning a response surface, estimating a statistical expectation, solving an optimization problem, etc., using only in a limited number of function evaluations. Under BODE methods, sequential design of experiments (SDOE) accomplishes this task by selecting an optimal sequence of experiments. SDOE methods use data-driven probabilistic surrogate models for emulating the expensive black-box function. Probabilistic predictions from the surrogate model are used to define an information acquisition function (IAF) which quantifies the marginal value contributed or the expected information gained by a hypothetical experiment. The next experiment is selected by maximizing the IAF. A generally applicable IAF is the expected information gain (EIG) about a QoI as captured by the expectation of the Kullback-Leibler divergence between the predictive distribution of the QoI after doing a hypothetical experiment and the current predictive distribution about the same QoI. Despite its intuitive appeal, applications of EIG have been limited due to the difficulty associated with estimating it.To overcome this barrier, in this work, we develop a practical numerical estimator of the EIG for arbitrary QoIs. We model the underlying information source as a fully-Bayesian, non-stationary Gaussian process (FB-NSGP), derive an approximation of the information gain of a hypothetical experiment about an arbitrary QoI conditional on the hyper-parameters, and estimate the EIG about the same QoI using sampling averages to integrate over the posterior of the hyper-parameters and the potential experimental outcomes. We demonstrate the performance of our method in four numerical examples and a practical engineering problem of steel wire manufacturing. The method is compared to two classic SDOE methods: random sampling and uncertainty sampling. The results show a mixed outcome where the proposed methods converges sooner with increasing

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Bayesian optimal experimental design for the Shock-tube experiment

Cited by 2 publications

References 15 publications

Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions

Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions

Learning Arbitrary Quantities of Interest from Expensive Black-Box Functions through Bayesian Sequential Optimal Design

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