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

作者：Perdikaris P; Venturi D; Royset J O; Karniadakis G E^*

来源：Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2015, 471(2179): 20150018.

DOI：10.1098/rspa.2015.0018

• surrogate modelling
• response surfaces
• risk-averse design
• uncertainty quantification
• machine learning
• big data

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.

• 出版日期2015-7-8