# Global Fitting of the Response Surface via Estimating Multiple Contours of a Simulator

## TL;DR

This paper introduces two innovative sequential design methods utilizing contour estimation to improve response surface fitting for computationally expensive simulators, enhancing prediction accuracy for risk assessment.

## Contribution

The paper presents novel sequential design strategies based on contour estimation to optimize input selection for better response surface approximation.

## Key findings

- Proposed methods outperform traditional designs in accuracy
- Numerical examples demonstrate improved prediction quality
- Approaches are effective for complex physical system simulations

## Abstract

Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known as experimental design, that is, how to select the input settings where the computer simulator is run and the corresponding response is collected. Extra care should be taken in the selection process because computer simulators can be computationally expensive to run. The selection shall acknowledge and achieve the goal of the analysis. This article focuses on the goal of producing more accurate prediction which is important for risk assessment and decision making. We propose two new methods of design approaches that sequentially select input settings to achieve this goal. The approaches make novel applications of simultaneous and sequential contour estimations. Numerical examples are employed to demonstrate the effectiveness of the proposed approaches.