Bayesian assimilation of multi-fidelity finite element models

A complex system can be modeled using various fidelities with the finite element method. A high-fidelity model is expected to be more computationally expensive compared to a low-fidelity model and in general may contain more degrees of freedom and more elements. This paper proposes a novel multi-fidelity approach to solve boundary value problems using the finite element method. A Bayesian approach based on Gaussian process emulators in conjunction with the domain decomposition method is developed. Using this approach one can seamlessly assimilate a low-fidelity model with a more expensive high-fidelity model. The idea is illustrated using elliptic boundary value problems.

► We propose a method to assimilate low-fidelity FE models with high-fidelity models.
► We couple Gaussian process emulators with domain decomposition methods.
► The computational cost of the associated Schur complement problem is reduced.
► The method is discussed and tested with different geometries.