
Speaker:

Alexander Litvinenko 

King Abdullah University of Science and Technology (KAUST), Saudi Arabia 
Date:

Tuesday, December 19, 2017 
Place:

USI Lugano Campus, room A13, Red building (Via G. Buffi 13) 
Time:

16:3017:30 


Abstract:

We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian loglikelihood function. To overcome cubic complexity in the linear algebra, we approximate the discretized covariance function in the hierarchical (H) matrix format. The Hmatrix format has a loglinear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations. The Hmatrix technique allows us to work with general covariance matrices in an ecient way, since Hmatrices can approximate inhomogeneous covariance functions, with a fairly general mesh that is not necessarily axesparallel, and neither the covariance matrix itself nor its inverse have to be sparse. We demonstrate our method with Monte Carlo simulations and an application to soil moisture data. The C, C++ codes and data are freely available.


Biography:

Alexander Litvinenko joined the Extreme Computing Research Center at KAUST, directed by David Keyes, in 2015. Before that he was a research scientist at the Uncertainty Quantification Center also at KAUST. He specializes in efficient numerical methods for stochastic PDEs, uncertainty quantification, and multilinear algebra. He is involved in Bayesian update methods for solving inverse problems, with the goal of reducing the complexity both the stochastic forward problem as well as the Bayesian update by a lowrank (sparse) tensor data approximation. Applications include aerodynamics, subsurface flow, and spatial statistics. Alexander earned B.S. (2000) and M.S. (2002) degrees in mathematics at Novosibirsk State University, and his PhD (2006) in the group of Prof. Hackbusch at MaxPlanckInstitut in Leipzig, on the combination of domain decomposition methods and hierarchical matrices for solving elliptic PDEs with jumping and oscillatory coefficients. From 20072013 he was a Postdoctoral Research Fellow at the TU Braunschweig in Germany.




Faculty of Informatics
Università della Svizzera italiana
Via Giuseppe Buffi 13
CH6904 Lugano
Tel.: +41 (0)58 666 46 90
Fax: +41 (0)58 666 45 36
Email: decanato.inf@usi.ch
Web: www.inf.usi.ch
Twitter: @USI_INF



