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

TL;DR

This paper introduces MSCE, a novel method for efficiently solving inverse problems for time series valued computer simulators, with applications in hydrology, enabling accurate parameter estimation and uncertainty quantification.

Contribution

The paper proposes a new multiple contour estimation approach (MSCE) for inverse problems in time series simulators, improving efficiency and uncertainty quantification over existing methods.

Findings

MSCE outperforms competitors in simulation studies.

Effective discretization of time series improves inverse problem solving.

Method successfully applied to real hydrological data.

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 (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.