Multi-fidelity Modelling via Recursive Co-kriging and Gasussian-Markov Random Fields

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Author
Royset, J.O.
Perdikaris, P.
Venturi, D.
Karniadakis, G.E.
Date
2015-06-02Metadata
Show full item recordAbstract
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.
Description
The article of record as published may be found at http://dx.doi.org/10.1098/rspa.2015.0018
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