A Bayesian framework for functional calibration of expensive computational models through non-isometric matching

Abstract

We study statistical calibration, i.e., adjusting features of a computational model that are not observable or controllable in its associated physical system. We focus on functional calibration, which arises in many manufacturing processes where the unobservable features, called calibration variables, are a function of the input variables. A major challenge in many applications is that computational models are expensive and can only be evaluated a limited number of times. Furthermore, without making strong assumptions, the calibration variables are not identifiable. We propose Bayesian Non-isometric Matching Calibration (BNMC) that allows calibration of expensive computational models with only a limited number of samples taken from a computational model and its associated physical system. BNMC replaces the computational model with a dynamic Gaussian process whose parameters are trained in the calibration procedure. To resolve the identifiability issue, we present the calibration problem from a geometric perspective of non-isometric curve to surface matching, which enables us to take advantage of combinatorial optimization techniques to extract necessary information for constructing prior distributions. Our numerical experiments demonstrate that in terms of prediction accuracy BNMC outperforms, or is comparable to, other existing calibration frameworks.

Keywords:

• Functional calibration
• Gaussian process
• Generalized minimum spanning tree

Acknowledgments

The authors acknowledge Chuck Zhang from Georgia Institute of Technology for providing the authors with the PVA-treated buckypaper fabrication data.

Additional information

Funding

Austin Buchanan is supported by the National Science Foundation under Grant No. 1662757. This work was completed utilizing the High Performance Computing Center facilities of Oklahoma State University at Stillwater.

Notes on contributors

Babak Farmanesh

Babak Farmanesh received his BS in industrial engineering from Sharif University of Technology in 2014, and his PhD from the School of Industrial Engineering and Management at Oklahoma State University in 2018. He is currently working as a Data Scientist at DELL Technologies. His research interest includes statistical machine learning, optimization, and operations research.

Arash Pourhabib

Arash Pourhabib received his BS in industrial engineering from Sharif University of Technology in 2008, and his PhD from the Department of Industrial and Systems Engineering at Texas A&M University in 2014. He is currently an adjunct assistant professor at the School of Industrial Engineering and Management at Oklahoma State University and a Data Scientist at Google. His research interests are in the areas of system informatics and statistical machine learning. He is a member of INFORMS and IISE.

Balabhaskar Balasundaram

Balabhaskar Balasundaram is an associate professor and the holder of Wilson Bentley Professorship in the School of Industrial Engineering and Management at Oklahoma State University. He received his B.Tech in mechanical engineering from the Indian Institute of Technology-Madras in 2002, and his PhD in industrial engineering from Texas A&M University in 2007. His research interests include combinatorial optimization and integer linear programming, specifically graph-theoretic models and their applications in social and biological network analysis. He is a member of IISE, INFORMS, SIAM, and MOS.

Austin Buchanan

Austin Buchanan is an assistant professor in the School of Industrial Engineering & Management at Oklahoma State University. In 2015, he received his PhD in industrial and systems engineering at Texas A&M University. His research interests are in network optimization and integer programming. He is a member of INFORMS and was recently awarded an NSF CAREER award.