  In this work we propose a low rank approximation of high fidelity finite
element simulations by utilizing weights corresponding to areas of high stress
levels for an abdominal aortic aneurysm, i.e. a deformed blood vessel. We focus
on the van Mises stress, which corresponds to the rupture risk of the aorta.
This is modeled as a Gaussian Markov random field and we define our
approximation as a basis of vectors that solve a series of optimization
problems. Each of these problems describes the minimization of an expected
weighted quadratic loss. The weights, which encapsulate the importance of each
grid point of the finite elements, can be chosen freely - either data driven or
by incorporating domain knowledge. Along with a more general discussion of
mathematical properties we provide an effective numerical heuristic to compute
the basis under general conditions. We explicitly explore two such bases on the
surface of a high fidelity finite element grid and show their efficiency for
compression. We further utilize the approach to predict the van Mises stress in
areas of interest using low and high fidelity simulations. Due to the high
dimension of the data we have to take extra care to keep the problem
numerically feasible. This is also a major concern of this work.
