Efficient approximation methods for random fields on manifolds

Uncertainty is all around us and caused, for example, by the nature of a problem as in quantum mechanics, the lack of our precise knowledge as in porous media, or inaccuracies in measurements.

While traditionally and due to the lack of computing power, science and technology relied on deterministic models, new developments allow to include randomness in the models. The new trend requires efficient simulation methods to sample the randomness.

In spatial problems such as weather predictions, ground water flows, and material surfaces, the randomness should be modeled by a random field.

The speed and the quality of the used sampling methods determine if the noisy models are applicable outside of academia.The purpose of this project is to develop and analyze efficient algorithms that approximate random fields with a given precision based on a prescribed covariance. By the end of the project new algorithms for nonstationary and anisotropic random fields on manifolds are delivered.

We will start with Gaussian fields and consider generalizations at a later stage of the project.

Based on earlier results for isotropic random fields on spheres, we are in a good starting position to extensions to Riemannian manifolds such as surfaces.The project will finance the project leaders research time and a PhD student.

Local and international collaborations complete the team and gather all necessary competences that guarantee the success of the project.