Multi-fidelity modelling via recursive co-kriging and Gaussian-Markov random fields

Proceedings. Mathematical, Physical, and Engineering Sciences
P PerdikarisG E Karniadakis

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.

Citations

Feb 26, 2016·Physics of Fluids·Paris PerdikarisGeorge Em Karniadakis
May 20, 2016·Journal of the Royal Society, Interface·Paris Perdikaris, George Em Karniadakis
Jan 7, 2020·PloS One·Paolo Di AchilleViatcheslav Gurev
Feb 20, 2020·Physical Review. E·Hongyu ZhengYao Zheng
Mar 2, 2021·Proceedings. Mathematical, Physical, and Engineering Sciences·J Del Águila FerrandisG E Karniadakis
Jun 15, 2019··Gorazd Medic, Gorazd Medic
Jun 24, 2018··Douglas L. AllaireSeyede Fatemeh Ghoreishi

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