The main research directions of the INM RAS are related to the scientific interests of its creator, Guri Ivanovich Marchuk. In 1980 there were four of them: numerical mathematics; simulation of atmospheric and oceanic dynamics; mathematical immunology and medicine; parallel computing. Currently, the research areas of the Institute has changed somewhat. Now it is computational mathematics, tensors and optimization methods; methods and technologies of numerical mathematics and problems of biology and medicine; modeling the Earth system dynamics and environmental problems; mathematical modeling of the atmosphere and ocean dynamics; and the variational data assimilation problems. Celebrating its 40th anniversary in 2020, the Marchuk Institute of Numerical Mathematics RAS is currently in consortium with Lomonosov Moscow State University, Keldysh Institute of Applied Mathematics RAS is part of the Moscow Center for Fundamental and Applied Mathematics.
The research directions of the INM RAS correspond to the Program of Fundamental Studies of the State Academies of Sciences for 2013–2020. In addition to 16 basic research topics, the Institute over the past 5 years has completed more than 100 various projects under the Programs of the Presidium and Departments of the Russian Academy of Sciences, Federal Target Programs, Programs of Ministries and Departments, Russian Foundation for Basic Research, Russian Science Foundation, and International Programs (https://www.inm.ras.ru). In the field of geophysical fluid dynamics, climate theory and environmental problems, the Institute actively cooperates with leading scientific teams of the Obukhov Institute of Atmospheric Physics RAS, Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Institute of Monitoring of Climate and Ecological Systems SB RAS, Shirshov Institute of Oceanology RAS, Moscow State University, Hydrometeorological Center of Russia, Marine Hydrophysical Institute RAS, Nuclear Safety Institute RAS, Zubov’s State Oceanographic Institute and other organizations.
Along with scientific research, the Institute pays more attention to scientific and pedagogical activities in the framework of the graduate school of the INM RAS and its two basic Chairs: Computing Technologies and Modeling in Geophysics and Mathematics at the Department of Control and Applied Mathematics of the Moscow Institute of Physics and Technology and Computing Technologies and Modeling—at the Faculty of Computational Mathematics and Cybernetics of Moscow State University. Of the 55 scientific staff at present, 29 graduates of the Moscow Institute of Physics and Technology and 11 at Moscow State University work at the INM RAS.
Guri Ivanovich said that in its activities, the INM RAS should follow the following principles: be aimed at solving important urgent problems; consist of three almost equal parts uniting researchers, graduate students and students; instead of traditional laboratories and departments, have a more flexible structure—creative research teams, the composition and subjects of which can change over time, following the challenges of modern science.