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Computer simulators are often used as a substitute of complex real-lifephenomena which are either expensive or infeasible to experiment with. Thispaper focuses on how to efficiently solve the inverse problem for an expensiveto evaluate time series valued computer simulator. The research is motivated bya hydrological simulator which has to be tuned for generating realisticrainfall-runoff measurements in Athens, Georgia, USA. Assuming that thesimulator returns g(x,t) over L time points for a given input x, the proposedmethodology begins with a careful construction of a discretization (time-)point set (DPS) of size $k << L$, achieved by adopting a regression splineapproximation of the target response series at k optimal knots locations$\{t^*_1, t^*_2, ..., t^*_k\}$. Subsequently, we solve k scalar valued inverseproblems for simulator $g(x,t^*_j)$ via the contour estimation method. Theproposed approach, named MSCE, also facilitates the uncertainty quantificationof the inverse solution. Extensive simulation study is used to demonstrate theperformance comparison of the proposed method with the popular competitors forseveral test-function based computer simulators and a real-life rainfall-runoffmeasurement model.

Solving an Inverse Problem for Time Series Valued Computer Simulators via Multiple Contour Estimation