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

Author

Farmanesh, Babak, Pourhabib, Arash, Balasundaram, Balabhaskar, and Buchanan, Austin

Subjects
Statistics - Machine Learning
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 (GP) 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., Comment: 39 pages; added analysis of residuals

Published
2015
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16. The minimum spanning k-core problem with bounded CVaR under probabilistic edge failures

Author

Ma, Juan, Pajouh, Foad Mahdavi, Balasundaram, Balabhaskar, and Boginski, Vladimir

Subjects
Computer networks -- Research, Engineering research, Information networks -- Research, Graphic methods -- Analysis, Mathematical optimization -- Research, Algorithms -- Research, Algorithm, Computers, Science and technology
Abstract

This article introduces the minimum spanning k-core problem that seeks to find a spanning subgraph with a minimum degree of at least k (also known as a k-core) that minimizes [...]

Published
2016
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35. A Bayesian framework for functional calibration of expensive computational models through non-isometric matching.

Author

Farmanesh, Babak, Pourhabib, Arash, Balasundaram, Balabhaskar, and Buchanan, Austin

Subjects
CALIBRATION, MANUFACTURING processes, COMBINATORIAL optimization, GAUSSIAN processes, MATHEMATICAL optimization, ISOMETRICS (Mathematics), FORECASTING
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. [ABSTRACT FROM AUTHOR]

Published
2021
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