GERMAN-RUSSIAN RESEARCH LABORATORY (GERRUS-LAB) High-dimensional Tensor Methods in Mathematical Sciences and Applications Methods in Mathematical Sciences and Applications

General     Operating Schemes     Board     Members     Collaborations     Publications     Events     Visits



PD, DrSci. Boris Khoromskij (PhD)

Max-Planck Institute for Mathematics in the Sciences (MPI MiS), Leipzig, Privat Dozent (PD) at the University of Leipzig


Prof. Eugene Tyrtyshnikov

Institute of Numerical Mathematics of Russian Academy of Sciences (INM RAS, Moscow), Lomonosov Moscow State University (MSU), Moscow Institute (Univeristy) of Physics and Technology (MIPT), Corresponding Member of RAS





High-dimensional tensor methods have become increasingly ubiquitous in various areas of applied, computational, and industrial mathematics. These include algebraic statistics, approximation theory, bioinformatics, psychometrics, chemometrics, computational finances, computational complexity, machine learning, pattern recognition, material sciences, quantum chemistry, quantum computing and stochastic PDEs.


A significant part of research topics is about application of matrix and linear algebra methods in tensor and multilinear problems. On the other hand, linear algebra problems on higher scales require special data structures and approaches using multilinear forms or tensors. Many applications become tractable as soon as we consider data to be approximated by rank structured tensors. This pertains to many numerical problems for PDEs and integro-differential equations, in particular to quantum chemistry computations.


The purpose of the joint laboratory is a triptich of advanced multilinear algebra, efficient tensor-structured numerical methods and modern high-dimensional applications. A special focus is on wide promotion of tensor methods in scientific and application communities. Particular areas and topics of research include:



methods of tensor approximation of multivariate functions and related operators


tensor-train, quantics and quantics-tensor-train methods


cross approximation methods in presence of missing data


advanced analytic and algebraic methods for computing tensor decompositions


tensor methods in potential theory, electron density computations, molecula dynamics


tensor methods in bioinformatics


tensor numerical methods for solving stochastic PDEs





GERRUS-LAB is based on the already existing facilities at the MPI MiS, Leipzig and INM RAS, Moscow. Its modus operandi includes exchange visits of researchers and master/PhD students, organization ans support of joint workshops, schools, lecture courses and other education activities, preparation and conduction of joint research projects, collaboration with other active research groups. The INM resources involve the PhD programmes of Russian Academy of Sciences, Government Contracts and Russian Basic Research Foundation grants. The MPI resources assume several PhD/Postdoc positions that are occupied by GERRUS-LAB members on a long- and middle-term basis with flexible visiting schemes within working research projects.



Prof. Reinhold Schneider (TU Berlin)

Prof. H. Yserentant (TU Berlin)

Prof. Volker Mehrmann (TU Berlin)

Prof. Christian Lubich (University of Tuebingen)

Prof. Christoph Schwab (ETH Zurich)

Prof. Stefan Sauter (University of Zurich)

Prof. Pierre Comon  (INRIA, Sofia-Antipolis)

Prof. Neville Ford (University of Chester, UK)

Prof. Vadim Olshevsky (University of Connecticut, USA)

Prof. Lieven De Lathauwer (University of Leuven)

Dr. Heinz-Jurgen Flad (TU Berlin)

Dr. Mike Espig (MPI MiS)

Prof. Ivan Gavrilyuk (BA Eisenach)

Dr. Gunther Schmidt (WIAS Berlin)

Dr. Nickolai Zamarashkin (INM RAS)

Dr. Sergei Goreinov (INM RAS)

Dr. Stas Stavtsev (INM RAS)

Dr. Tamara Kolda (Sandia National Laboratories in Livermore, California)

Dr. Lek-Heng Lim (University of Berkeley, USA)

PhD student Cristobal Bertoglio (University Paris-VI)