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

• 成果类型: Article; Early Access
• 署名作者: Nie, Xiao; Chien, Peter; Morgan, Dane; Kaczmarowski, Amy
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1654876
• 发表日期: 2019
• 关键词: molecular-fields; potentials; designs

摘要

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.