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

Computer simulators are often used as a substitute of complex real-life phenomena, which either expensive or infeasible to experiment with. This paper focuses on how efficiently solve the inverse problem for an evaluate time-series-valued computer simulator. The research is motivated by hydrological simulator has be tuned generating realistic rainfall–runoff measurements in Athens, Georgia, USA. Assuming that returns g(x, t) over L time points given input x, proposed methodology begins with careful construction discretization (time-) point set size $$k \ll L$$ , achieved adopting regression spline approximation target response series at k optimal knot locations $$\{t_1^*, t_2^*,\ldots ,t_k^*\}$$ . Subsequently, we scalar-valued problems $$g(x,t_j^*)$$ via contour estimation method. approach, named MSCE, also facilitates uncertainty quantification solution. Extensive simulation study demonstrate performance comparison method popular competitors several test-function-based and measurement model.