My current research interests are: efficient numerical methods for solving multi-parametric/stochastic PDEs; multi-linear algebra for analyzing of large data and low-rank/sparse tensor methods for uncertainty quantification; uncertainty quantification in inverse problems and data assimilation; and spatio-temporal statistics. My research is motivated by real-world applications in the areas of subsurface hydrology, oil recovery, vadoze zone hydrology, aerospace engineering, and so on. I have made some important contributions to: fast numerical techniques using low-rank tensor approximations to solve stochastic PDEs; inexpensive functional generalized polynomial approximation of classical Bayesian update formula; theory and numerical methods for approximation of large covariance matrices in spatial statistics using low-rank concepts; probabilistic/stochastic methods to model and quantify uncertainties in coefficients, parameters and computational geometry. I have collaborated with researchers from different areas including geoscientists, engineers, and statisticians.
I earned B.S. and M.S. degrees working on data analysis in Sobolev Institute of Mathematics at the Novosibirsk State University. During my undergraduate study, my research interests were related to the building of optimal decision trees for various areas of applications [22-27].
I did my PhD in a group of Prof. Hackbusch at Max-Planck-Institut fuer Mathematik in Leipzig, Germany. My Ph.D. research focus was a combination of domain decomposition methods and hierarchical matrices for solving elliptic PDEs with jumping and strongly oscillatory coefficients . This results in the hierarchical domain decomposition (HDD) method, which can be used for partial evaluation of the discrete solution of an elliptic problem. The resulting method constructs the discrete solution operator for each node of the hierarchical/recursive domain decomposition tree. This operator is applied to the given boundary values and a source term and evaluate the solution on the interface/skeletons. The HDD method allows computing the solution on different scales and truncating components related to small subdomains. The HDD approach is, in particular, well suited for problems with oscillatory coefficients where reduced-order modelling for representing the small oscillations is needed. Matrix operations (e.g., matrix-matrix product, matrix inverse, the Schur complement) are done in the hierarchical matrix format with the computational cost O(nlog n), where n is the number of unknowns.