Fast sampling from parameterised Gaussian random fields

Add to your list(s) Download to your calendar using vCal

• Jonas Latz (Technische Universität München)
• Friday 16 February 2018, 11:00-13:00
• Seminar Room 2, Newton Institute.

If you have a question about this talk, please contact INI IT.

This talk has been canceled/deleted

Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and covariance operator. In more complex models these can also be partially unknown. Then we need to handle a family of Gaussian random fields indexed with hyperparameters. Sampling for a fixed configuration of hyperparameters is already very expensive, as it requires a Cholesky or spectral decomposition of the discretised covariance operator, which is in general a large dense matrix. Sampling from multiple configurations increases the total computational cost severely.     In this report we construct a reduced basis surrogate for parameterised Karhunen-Loève expansions – upon which our sampling procedure relies. The reduced basis is built using snapshots of Karhunen-Loève eigenvectors. In particular, we consider Matern type covariance operators with unknown correlation length and standard deviation. We suggest a linearisation of the covariance function and describe the associated online-offline decomposition. In numerical experiments, we investigate the approximation error of the reduced eigenpairs. As an application, we consider forward uncertainty propagation and Bayesian inversion in an elliptic PDE , where the log of the diffusion coefficient is a parameterised Gaussian random field. We discretise PDE operators and covariance operators with finite elements. In the Bayesian inverse problem we employ a Markov Chain Monte Carlo method on the reduced space to generate samples from the posterior measure. All numerical experiments are done in 2D space with non-separable covariance operators on finite element grids with tens of thousands of degrees of freedom.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

This talk is not included in any other list

Note that ex-directory lists are not shown.