Inverse Problem for Dynamic Computer Simulators via Multiple Scalar-valued Contour Estimation
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In this paper we consider a dynamic computer simulator that produces a time-series response y_t(x) over L time points, for every given input parameter x. We propose a method for solving inverse problems, which refer to the finding of a set of inputs that generates a pre-specified simulator output. Inspired by the sequential approach of contour estimation via expected improvement criterion developed by Ranjan et al. (2008, DOI: 10.1198/004017008000000541), our proposed method discretizes the target response series on k (≪ L) time points, and then iteratively solves k scalar-valued inverse problems with respect to the discretized targets. We also propose to use spline smoothing of the target response series to identify the optimal number of knots, k, and the actual location of the knots for discretization. The performance of the proposed methods is compared for several test-function based computer simulators and the motivating real application that uses a rainfall-runoff measurement model named Matlab-Simulink model.
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