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