Sequential Design of Computer Experiments

Ginsbourger, David

doi:10.1002/9781118445112.stat08124

Cited by 12 publications

(14 citation statements)

References 78 publications

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“…Comparing SDoE methods from the literature (Kushner, 1964;Jones et al, 1998;Williams et al, 2000;Bichon et al, 2008;Ranjan et al, 2008;Picheny et al, 2010;Bect et al, 2012;Mockus, 2012;Balesdent et al, 2013;Shahriari et al, 2016;Sinsbeck and Nowak, 2017;Ginsbourger, 2018), we find that they all share the same general structure. They all revolve around a quantity of interest QoI = q (u) that depends on a computationally expensive function u.…”

Section: Sequential Design Of Computer Experiments: General Structurementioning

confidence: 83%

Exploratory-Phase-Free Estimation of GP Hyperparameters in Sequential Design Methods—At the Example of Bayesian Inverse Problems

Sinsbeck

Höge

Nowak

2020

Front. Artif. Intell.

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Methods for sequential design of computer experiments typically consist of two phases. In the first phase, the exploratory phase, a space-filling initial design is used to estimate hyperparameters of a Gaussian process emulator (GPE) and to provide some initial global exploration of the model function. In the second phase, more design points are added one by one to improve the GPE and to solve the actual problem at hand (e.g., Bayesian optimization, estimation of failure probabilities, solving Bayesian inverse problems). In this article, we investigate whether hyperparameters can be estimated without a separate exploratory phase. Such an approach will leave hyperparameters uncertain in the first iterations, so the acquisition function (which tells where to evaluate the model function next) and the GPE-based estimator need to be adapted to non-Gaussian random fields. Numerical experiments are performed exemplarily on a sequential method for solving Bayesian inverse problems. These experiments show that hyperparameters can indeed be estimated without an exploratory phase and the resulting method works almost as efficient as if the hyperparameters had been known beforehand. This means that the estimation of hyperparameters should not be the reason for including an exploratory phase. Furthermore, we show numerical examples, where these results allow us to eliminate the exploratory phase to make the sequential design method both faster (requiring fewer model evaluations) and easier to use (requiring fewer choices by the user).

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Section: Sequential Design Of Computer Experiments: General Structurementioning

confidence: 83%

Exploratory-Phase-Free Estimation of GP Hyperparameters in Sequential Design Methods—At the Example of Bayesian Inverse Problems

Sinsbeck

Höge

Nowak

2020

Front. Artif. Intell.

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“…Note that the value of standard deviation σ does not affect the kriging estimate G (x), but affects the kriging error (14).…”

Section: Discussionmentioning

confidence: 99%

Applying kriging proxies for Markov chain Monte Carlo in reservoir simulation

2020

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One way to quantify the uncertainty in Bayesian inverse problems arising in the engineering domain is to generate samples from the posterior distribution using Markov chain Monte Carlo (MCMC) algorithms. The basic MCMC methods tend to explore the parameter space slowly, which makes them inefficient for practical problems. On the other hand, enhanced MCMC approaches, like Hamiltonian Monte Carlo (HMC), require the gradients from the physical problem simulator, which are often not available. In this case, a feasible option is to use the gradient approximations provided by the surrogate (proxy) models built on the simulator output. In this paper, we consider proxy-aided HMC employing the Gaussian process (kriging) emulator. We overview in detail the different aspects of kriging proxies, the underlying principles of the HMC sampler and its interaction with the proxy model. The proxy-aided HMC algorithm is thoroughly tested in different settings, and applied to three case studies-one toy problem, and two synthetic reservoir simulation models. We address the question of how the sampler performance is affected by the increase of the problem dimension, the use of the gradients in proxy training, the use of proxy-for-the-data and the different approaches to the design points selection. It turns out that applying the proxy model with HMC sampler may be beneficial for relatively small physical models, with around 20 unknown parameters. Such a sampler is shown to outperform both the basic Random Walk Metropolis algorithm, and the HMC algorithm fed by the exact simulator gradients.

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“…. ., x n 0 ) (see, e.g., Dupuy et al, 2015) and evaluating f X n 0 to initialize the knowledge of the algorithm (e.g., n 0 = 9 blue dots in the left panel of Fig. 4a).…”

Section: Optimization Methodologymentioning

confidence: 99%

“…In this group of methods, less information about the contaminant plume is required and the method can be adapted to uncertain geology (Zhang et al, 2016). To the best of our knowledge, existing studies using forward-solver-based approaches were limited to homogeneous (Datta et al, 2011;Hansen and Vesselinov, 2016) or multi-Gaussian-like (Aral et al, 2001;Ayvaz, 2016) heterogeneous property fields.…”

Section: Introductionmentioning

confidence: 99%

“…Within this last set of methods, different optimization techniques can be employed. Classical nonlinear optimization techniques following a derivative-based approach (Mahar and Datta, 2000;Datta et al, 2011), such as the Levenberg-Marquardt algorithm (Hansen and Vesselinov, 2016), present the risk of being stuck in local minima. Employing a tabu search algorithm (Yeh et al, 2007) presents the same inconvenience as it iteratively explores neighbor solutions.…”

Section: Introductionmentioning

confidence: 99%

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Contaminant source localization via Bayesian global optimization

Pirot

Krityakierne

Ginsbourger

et al. 2019

Hydrol. Earth Syst. Sci.

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Contaminant source localization problems require efficient and robust methods that can account for geological heterogeneities and accommodate relatively small data sets of noisy observations. As realism commands hi-fidelity simulations, computation costs call for global optimization algorithms under parsimonious evaluation budgets. Bayesian optimization approaches are well adapted to such settings as they allow the exploration of parameter spaces in a principled way so as to iteratively locate the point(s) of global optimum while maintaining an approximation of the objective function with an instrumental quantification of prediction uncertainty. Here, we adapt a Bayesian optimization approach to localize a contaminant source in a discretized spatial domain. We thus demonstrate the potential of such a method for hydrogeological applications and also provide test cases for the optimization community. The localization problem is illustrated for cases where the geology is assumed to be perfectly known. Two 2-D synthetic cases that display sharp hydraulic conductivity contrasts and specific connectivity patterns are investigated. These cases generate highly nonlinear objective functions that present multiple local minima. A derivative-free global optimization algorithm relying on a Gaussian process model and on the expected improvement criterion is used to efficiently localize the point of minimum of the objective functions, which corresponds to the contaminant source location. Even though concentration measurements contain a significant level of proportional noise, the algorithm efficiently localizes the contaminant source location. The variations of the objective function are essentially driven by the geology, followed by the design of the monitoring well network. The data and scripts used to generate objective functions are shared to favor reproducible research. This contribution is important because the functions present multiple local minima and are inspired from a practical field application. Sharing these complex objective functions provides a source of test cases for global optimization benchmarks and should help with designing new and efficient methods to solve this type of problem.

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Sequential Design of Computer Experiments

Cited by 12 publications

References 78 publications

Exploratory-Phase-Free Estimation of GP Hyperparameters in Sequential Design Methods—At the Example of Bayesian Inverse Problems

Exploratory-Phase-Free Estimation of GP Hyperparameters in Sequential Design Methods—At the Example of Bayesian Inverse Problems

Applying kriging proxies for Markov chain Monte Carlo in reservoir simulation

Contaminant source localization via Bayesian global optimization

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