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

Christoph Striegel, Jonas Biehler, Wolfgang A. Wall, Göran Kauermann

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish
Pages (from-to)279-290
Number of pages12
JournalTechnometrics
Volume64
Issue number3
DOIs
StatePublished - 2022

Keywords

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

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