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A Survey of Constrained Gaussian Process: Approaches and Implementation Challenges

Journal Article · · Journal of Machine Learning for Modeling and Computing
 [1];  [1];  [2];  [2];  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
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Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a larger effort in scientific machine learning, many recent works have incorporated physical constraints or other a priori information within Gaussian process regression to supplement limited data and regularize the behavior of the model. We provide an overview and survey of several classes of Gaussian process constraints, including positivity or bound constraints, monotonicity and convexity constraints, differential equation constraints provided by linear PDEs, and boundary condition constraints. We compare the strategies behind each approach as well as the differences in implementation, concluding with a discussion of the computational challenges introduced by constraints.
Research Organization:
Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000; NA0003525
OSTI ID:
1691455
Alternate ID(s):
OSTI ID: 1725870
Report Number(s):
SAND--2020-11308J; SAND--2020-6086J; 691556
Journal Information:
Journal of Machine Learning for Modeling and Computing, Journal Name: Journal of Machine Learning for Modeling and Computing Journal Issue: 2 Vol. 1; ISSN 2689-3967
Publisher:
Begell HouseCopyright Statement
Country of Publication:
United States
Language:
English

References (2)

Monotone Smoothing with Application to Dose-Response Curves and the Assessment of Synergism journal December 1990
Hilbert Space Methods for Reduced-Rank Gaussian Process Regression text January 2014

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97 MATHEMATICS AND COMPUTING