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 language | English |
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Pages (from-to) | 279-290 |
Number of pages | 12 |
Journal | Technometrics |
Volume | 64 |
Issue number | 3 |
DOIs | |
State | Published - 2022 |
Keywords
- Computer experiments
- Functional data analysis
- Gaussian Markov random fields
- Multifidelity simulations
- Multivariate data
- Spatial Statistics