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

Striegel, Christoph; Biehler, Jonas; Wall, Wolfgang A. und Kauermann, Goeran (2022): A Multifidelity Function-on-Function Model Applied to an Abdominal Aortic Aneurysm. In: Technometrics, Bd. 64, Nr. 3: S. 279-290

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-Loeve decomposition. Our model enables real multivariate predictions on the complete grid instead of resorting to the outcome of specific points.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Statistik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0040-1706
• Sprache: Englisch