Enhancing Simulation Metamodeling with Domain Knowledge and Regularization

Project: Research

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Simulation is used extensively to facilitate decision making processes in many areasincluding health care, finance, manufacturing, logistics, telecommunication, etc. However,simulation models are often computationally expensive to execute, severely restrictingthe usefulness of simulation in settings such as real-time decision making and systemoptimization.Metamodeling has been actively developed in the simulation community to alleviatecomputational inefficiency. The basic concept is that the user executes the simulationmodel only at a small number of carefully selected “design points”. A metamodel can bebuilt to approximate the true response surface by interpolating the simulation outputs.The responses at other points are then predicted by the metamodel without running thesimulation at all, thereby substantially reducing the computational costs. However,existing metamodels usually treat the simulation model as a black box, discarding thestructural properties of the response surface. Therefore, they often fail to capture highlynonlinear response surfaces, which may lead to a misleading decision concerning astochastic system of interest.The proposed research will address this defect of simulation metamodeling in order togive more reliable simulation-based decisions in dynamic environments. We propose anew metamodeling technique called regularized stochastic kriging, which builds on twocentral concepts. One is to incorporate an analytical model that admits a closed-formsolution at the cost of (overly) simplifying assumptions. Representing the domainknowledge of the stochastic system, this analytical model is expected to provide a roughapproximation of the nonlinear trend, removing a great portion of variation of theresponse surface. The other is to use general-purpose basis functions to characterize the“detrended” surface, i.e. the difference between the analytical model and the trueresponse surface. We will use regularized regression to select the significant basisfunctions automatically from a potentially large collection to avoid overfitting.In this project, we will develop a comprehensive methodology for the new metamodel.First, we will develop a penalized maximum likelihood estimation (PMLE) scheme forestimating the unknown parameters. Second, we will establish the large-sampleproperties of PMLE, including sparsity and asymptotic normality. The sparsity willguarantee that insignificant basis functions would be excluded asymptotically. Third, wewill devise efficient algorithms for computationally solving the PMLE problem. Finally,we will show that the PMLE scheme can substantially reduce the variance of theprediction at the cost of introducing a small bias, thereby improving the overallprediction accuracy in terms of the mean squared error.


Project number9042757
Grant typeGRF
Effective start/end date1/07/171/06/19