Extending Multifidelity Models Using Normalizing Flows

A common situation in statistical computer experiments is when we have multiple models for the same phenomenon, where accuracy and computational cost vary across the different models. Kennedy and O'Hagan (2000) popularized a framework for this 'multi-fidelity problem' that relates the different models in a linear way using Gaussian processes, which was then extended to the nonlinear setting in Perdikaris et al. (2017). In this work, we further extend this framework by using normalizing flows. Normalizing flows are a method of statistical inference where we transform a simple 'base' distribution into a more complex distribution with a series of invertible and differentiable transformations (see e.g. Papamakarios et al. 2020). We show results from numerical studies showing that using normalizing flows for this problem performs well and is flexible.

Multifidelity Modeling

Computer Experiments

Normalizing Flows 

Section on Physical and Engineering Sciences