Multi-fidelity methods for uncertainty quantification in transport problems

We compare several multi-fidelity approaches for uncertainty quantification in flow and transport simulations that have a lower computational cost than the standard Monte Carlo method. The cost reduction is achieved by combining a small number of high-resolution (high-fidelity) simulations with a large number of low-resolution (low-fidelity) simulations. We propose a new method, a re-scaled Multi Level Monte Carlo (rMLMC) method. The rMLMC is based on the idea that the statistics of quantities of interest depends on scale/resolution. We compare rMLMC with existing multi-fidelity methods such as Multi Level Monte Carlo (MLMC) and reduced basis methods and discuss advantages of each approach.