Gaussian process regression constrained by boundary value problems

Gulian, M.; Frankel, A.; Swiler, L.

doi:10.1016/j.cma.2021.114117

Gaussian process regression constrained by boundary value problems

Journal Article · Mon Oct 25 00:00:00 EDT 2021 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2021.114117· OSTI ID:1831157

Gulian, M. ^[1]; Frankel, A. ^[2]; Swiler, L. ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sandia National Lab. (SNL-CA), Livermore, CA (United States)

We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and boundary conditions, but for which only scattered observations of the source term are available. Scattered observations of the solution may also be used in the regression. The framework combines co-kriging with the linear transformation of a Gaussian process together with the use of kernels given by spectral expansions in eigenfunctions of the boundary value problem. Furthermore, it benefits from a reduced-rank property of covariance matrices. We demonstrate that the resulting framework yields more accurate and stable solution inference as compared to physics-informed Gaussian process regression without boundary condition constraints.

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: NA0003525

OSTI ID:: 1831157

Alternate ID(s):: OSTI ID: 1828217

Report Number(s):: SAND--2021-10889J; 699825

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 388; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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42 ENGINEERING
Boundary condition
Boundary value problem
Constrained Gaussian process
Physics-informed
Scientific machine learning

Gaussian process regression constrained by boundary value problems

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