A Multifidelity Function-on-Function Model Applied to an Abdominal Aortic Aneurysm. Issue 3 (3rd July 2022)

• Record Type: Journal Article
• Authors: Striegel, Christoph; Biehler, Jonas; Wall, Wolfgang A.; Kauermann, Göran
• Is Part Of: Technometrics. Volume 64:Issue 3(2022)
• Page Start: 279
• Page End: 290
• Publication Date: 2022-07-03
• Subjects: Computer experiments -- Functional data analysis -- Gaussian Markov random fields -- Multifidelity simulations -- Multivariate data -- Spatial Statistics; Statistical physics -- Periodicals; Chemistry -- Statistical methods -- Periodicals; Engineering -- Statistical methods -- Periodicals; 519.5
• DOI: 10.1080/00401706.2021.2024453
• Languages: English
• ISSNs: 0040-1706

Abstract

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.