A Statistical Method for Emulation of Computer Models With Invariance-Preserving Properties, With Application to Structural Energy Prediction

Abstract

Statistical design and analysis of computer experiments is a growing area in statistics. Computer models with structural invariance properties now appear frequently in materials science, physics, biology, and other fields. These properties are consequences of dependency on structural geometry, and cannot be accommodated by standard statistical emulation methods. In this article, we propose a statistical framework for building emulators to preserve invariance. The framework uses a weighted complete graph to represent the geometry and introduces a new class of function, called the relabeling symmetric functions, associated with the graph. We establish a characterization theorem of the relabeling symmetric functions and propose a nonparametric kernel method for estimating such functions. The effectiveness of the proposed method is illustrated by examples from materials science. Supplemental material for this article can be found online.

Keywords:

• Analysis of designed experiments
• Computer experiments
• Experimental design

Acknowledgments

The authors thank the editor, AE, and two reviewers for useful comments that have led to improvement in the article.

Additional information

Funding

This material is based upon work supported by, or in part by, NSF grant DMS 1564376 and the NSF Software Infrastructure of Sustained Innovation (SI2) grant 1148011.