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

Abstract

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 of size $$k \ll L$$ , achieved by adopting a regression spline approximation of the target response series at k optimal knot locations $$\{t_1^*, t_2^*,\ldots ,t_k^*\}$$ . 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.