Multi-fidelity Modelling via Recursive Co-kriging and Gasussian-Markov Random Fields
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Authors
Royset, J.O.
Perdikaris, P.
Venturi, D.
Karniadakis, G.E.
Subjects
surrogate modelling
response surfaces
risk-averse design
uncertainty quantification
machine learning
big data
response surfaces
risk-averse design
uncertainty quantification
machine learning
big data
Advisors
Date of Issue
2015-06-02
Date
June 2, 2015
Publisher
Royal Society
Language
Abstract
We propose a new framework for design under
uncertainty based on stochastic computer simulations
and multi-level recursive co-kriging. The proposed
methodology simultaneously takes into account
multi-fidelity in models, such as direct numerical
simulations versus empirical formulae, as well as
multi-fidelity in the probability space (e.g. sparse grids
versus tensor product multi-element probabilistic
collocation). We are able to construct response surfaces
of complex dynamical systems by blending
multiple information sources via auto-regressive
stochastic modelling. A computationally efficient
machine learning framework is developed based on
multi-level recursive co-kriging with sparse precision
matrices of Gaussian–Markov random fields. The
effectiveness of the new algorithms is demonstrated in
numerical examples involving a prototype problem in
risk-averse design, regression of random functions, as
well as uncertainty quantification in fluid mechanics
involving the evolution of a Burgers equation from
a random initial state, and random laminar wakes
behind circular cylinders.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.1098/rspa.2015.0018
Series/Report No
Department
Operations Research (OR)
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
DARPA grant HR0011-14-1-0060
AFOSR grant FA9550-12-1-0463
Argonne Leadership Computing Facility (ALCF)
DARPA grant HR001-14-1-225
AFOSR grant FA9550-12-1-0463
Argonne Leadership Computing Facility (ALCF)
DARPA grant HR001-14-1-225
Funder
DARPA grant HR0011-14-1-0060
AFOSR grant FA9550-12-1-0463
DARPA grant HR001-14-1-225
AFOSR grant FA9550-12-1-0463
DARPA grant HR001-14-1-225
Format
23 p.
Citation
P. Perdikaris, D. Venturi, J.O. Royset, and G. Karniadakis, 2015, "Multi-fidelity modeling via recursive co-kriging and Gaussian Markov random fields," Royal Society Proceedings A, Vol. 2179, No. 471.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.