A Multifidelity Function-on-Function Model Applied to an Abdominal Aortic Aneurysm

Abstract

In this work, we predict the outcomes of high fidelity multivariate computer simulations from low fidelity counterparts using function-to-function regression. The high fidelity simulation takes place on a high definition mesh, while its low fidelity counterpart takes place on a coarsened and truncated mesh. We showcase our approach by applying it to a complex finite element simulation of an abdominal aortic aneurysm which provides the displacement field of a blood vessel under pressure. In order to link the two multidimensional outcomes we compress them and then fit a function-to-function regression model. The data are high dimensional but of low sample size, meaning that only a few simulations are available, while the output of both low and high fidelity simulations is in the order of several thousands. To match this specific condition our compression method assumes a Gaussian Markov random field that takes the finite element geometry into account and only needs little data. In order to solve the function-to-function regression model we construct an appropriate prior with a shrinkage parameter which follows naturally from a Bayesian view of the Karhunen–Loève decomposition. Our model enables real multivariate predictions on the complete grid instead of resorting to the outcome of specific points.

Keywords:

• Computer experiments
• Functional data analysis
• Gaussian Markov random fields
• Multifidelity simulations
• Multivariate data
• Spatial Statistics

Supplementary Materials

Code and Data: repro_code.zip is a compressed folder that contains code and data to reproduce the results on a small subset of the data used in the article. The full dataset is available at: https://syncandshare.lrz.de/getlink/fi2soSUsR5PzuLnN6Rx8kZ6L/.

Probabilistic Material Model: probabilistic_material_model. pdf contains further details on the finite element simulation with a focus on the modeling of wall parameters.