Inverse problem for time-series valued computer model via scalarization

TL;DR

This paper addresses the challenge of estimating inverse solutions for expensive time-series valued computer simulators, extending previous scalar-based methods to handle complex temporal outputs.

Contribution

It introduces a novel approach for inverse problems involving time-series outputs, building upon scalarization techniques for more effective estimation.

Findings

The proposed method performs well on simulated examples.

Application to real data demonstrates practical utility.

Outperforms existing scalar-based inverse estimation methods.

Abstract

For an expensive to evaluate computer simulator, even the estimate of the overall surface can be a challenging problem. In this paper, we focus on the estimation of the inverse solution, i.e., to find the set(s) of input combinations of the simulator that generates (or gives good approximation of) a pre-determined simulator output. Ranjan et al. (2008) proposed an expected improvement criterion under a sequential design framework for the inverse problem with a scalar valued simulator. In this paper, we focus on the inverse problem for a time-series valued simulator. We have used a few simulated and two real examples for performance comparison.