Sequential design of computer experiments for the estimation of a probability of failure

This paper deals with the problem of estimating the volume of the excursion set of a function $f:\mathbb{R}^d \to \mathbb{R}$ above a given threshold, under a probability measure on $\mathbb{R}^d$ that is assumed to be known. In the industrial world, this corresponds to the problem of estimating a probability of failure of a system. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. One of the main contributions of this article is to derive SUR (stepwise uncertainty reduction) strategies from a Bayesian-theoretic formulation of the problem of estimating a probability of failure. These sequential strategies use a Gaussian process model of $f$ and aim at performing evaluations of $f$ as efficiently as possible to infer the value of the probability of failure. We compare these strategies to other strategies also based on a Gaussian process model for estimating a probability of failure.Comment: This is an author-generated postprint version. The published version is available at http://www.springerlink.co

On Bayesian Search for the Feasible Space Under Computationally Expensive Constraints

We are often interested in identifying the feasible subset of a decision space under multiple constraints to permit effective design exploration. If determining feasibility required computationally expensive simulations, the cost of exploration would be prohibitive. Bayesian search is data-efficient for such problems: starting from a small dataset, the central concept is to use Bayesian models of constraints with an acquisition function to locate promising solutions that may improve predictions of feasibility when the dataset is augmented. At the end of this sequential active learning approach with a limited number of expensive evaluations, the models can accurately predict the feasibility of any solution obviating the need for full simulations. In this paper, we propose a novel acquisition function that combines the probability that a solution lies at the boundary between feasible and infeasible spaces (representing exploitation) and the entropy in predictions (representing exploration). Experiments confirmed the efficacy of the proposed function

On the Use of Upper Trust Bounds in Constrained Bayesian Optimization Infill Criterion

In order to handle constrained optimization problems with a large number of design variables, a new approach has been proposed to address constraints in a surrogate-based optimization framework. This approach focuses on sequential enrichment using adaptive surrogate models based on Bayesian optimization approach, and Gaussian process models. A constraints criterion using the uncertainty estimation of the Gaussian process models is introduced. Different evolutions of the algorithm, based on the accuracy of the constraints surrogate models, are used for selecting the infill sample points. The resulting algorithm has been tested on the well known modified Branin optimization problem

Communications Biophysics

Contains reports on four research projects.National Institutes of Health (Grant 5 P01 NS13126-02)National Institutes of Health (Grant 5 K04 NS00113-03)National Institutes of Health (Grant 2 ROI NS11153-02A1)National Science Foundation (Grant BNS77-16861)National Institutes of Health (Grant 5 RO1 NS10916-03)National Institutes of Health (Fellowship 1 F32 NS05327)National Institutes of Health (Grant 5 ROI NS12846-02)National Institutes of Health (Fellowship 1 F32 NS05266)Edith E. Sturgis FoundationNational Institutes of Health (Grant 1 R01 NS11680-01)National Institutes of Health (Grant 2 RO1 NS11080-04)National Institutes of Health (Grant 5 T32 GIM107301-03)National Institutes of Health (Grant 5 TOI GM01555-10

Communications Biophysics

Contains reports on ten research projects.National Institutes of Health (Grant 5 P01 NS13126)National Institutes of Health (Training Grant 5 T32 NS0704)National Science Foundation (Grant BNS80-06369)National Institutes of Health (Grant 5 R01 NS11153)National Science Foundation (Grant BNS77-16861)National Institutes of Health (Grant 5 RO1 NS12846)National Science Foundation (Grant BNS77-21751)National Institutes of Health (Grant 1 P01 NS14092)Karmazin Foundation through the Council for the Arts at MITNational Institutes of Health (Fellowship 5 F32 NS06386)National Science Foundation (Fellowship SP179-14913)National Institutes of Health (Grant 5 RO1 NS11080

Communications Biophysics

Contains research objectives and summary of research on nine research projects split into four sections.National Institutes of Health (Grant 5 ROI NS11000-03)National Institutes of Health (Grant 1 P01 NS13126-01)National Institutes of Health (Grant 1 RO1 NS11153-01)National Institutes of Health (Grant 2 R01 NS10916-02)Harvard-M.I.T. Rehabilitation Engineering CenterU. S. Department of Health, Education, and Welfare (Grant 23-P-55854)National Institutes of Health (Grant 1 ROl NS11680-01)National Institutes of Health (Grant 5 ROI NS11080-03)M.I.T. Health Sciences Fund (Grant 76-07)National Institutes of Health (Grant 5 T32 GM07301-02)National Institutes of Health (Grant 5 TO1 GM01555-10

Communications Biophysics

Contains reports on nine research projects split into four sections.National Institutes of Health (Grant 5 PO1 NS13126)National Institutes of Health (Grant 5 KO4 NS00113)National Institutes of Health (Training Grant 5 T32 NS07047)National Institutes of Health (Training Grant 1 T32 NS07099)National Science Foundation (Grant BNS77-16861)National Institutes of Health (Grant 5 ROI NS10916)National Institutes of Health (Grant 5 RO1 NS12846)National Science Foundation (Grant BNS77-21751)National Institutes of Health (Grant 1 RO1 NS14092)Edith E. Sturgis FoundationHealth Sciences FundNational Institutes of Health (Grant 2 R01 NS11680)National Institutes of Health (Fellowship 5 F32 NS05327)National Institutes of Health (Grant 2 ROI NS11080)National Institutes of Health (Training Grant 5 T32 GM07301

Communications Biophysics

Contains reports on nine research projects split into four sections.National Institutes of Health (Grant 5 P01 NS13126)National Institutes of Health (Grant 5 K04 NS00113)National Institutes of Health (Training Grant 5 T32 NS07047)National Institutes of Health (Grant 5 ROl NS11153-03)National Institutes of Health (Fellowship 1 T32 NS07099-01)National Science Foundation (Grant BNS77-16861)National Institutes of Health (Grant 5 ROl NS10916)National Institutes of Health (Grant 5 ROl NS12846)National Science Foundation (Grant BNS77-21751)National Institutes of Health (Grant 1 RO1 NS14092)Health Sciences FundNational Institutes of Health (Grant 2 R01 NS11680)National Institutes of Health (Grant 2 RO1 NS11080)National Institutes of Health (Training Grant 5 T32 GM07301

Communications Biophysics

Contains reports on eight research projects split into four sections.National Institutes of Health (Grant 5 P01 NS13126)National Institutes of Health (Grant 5 K04 NS00113)National Institutes of Health (Training Grant 5 T32 NS07047)National Science Foundation (Grant BNS80-06369)National Institutes of Health (Grant 5 ROl NS11153)National Institutes of Health (Fellowship 1 F32 NS06544)National Science Foundation (Grant BNS77-16861)National Institutes of Health (Grant 5 R01 NS10916)National Institutes of Health (Grant 5 RO1 NS12846)National Science Foundation (Grant BNS77-21751)National Institutes of Health (Grant 1 R01 NS14092)National Institutes of Health (Grant 2 R01 NS11680)National Institutes of Health (Grant 5 ROl1 NS11080)National Institutes of Health (Training Grant 5 T32 GM07301