Leaders: Adam GheorgheDSc (Physics & Maths), ProfessorBuša JánPhD (Physics & Maths), Associate Professor Development and use of mathematical and computer methods for modeling new experimental facilities, accelerator complexes and their elements, nuclear-physical processes, complex physical systems. - Three-dimensional computer simulation of magnetic field distributions in superconducting dipole and quadrupole magnets for the projects NICA (JINR) and FAIR (GSI). - Simulation of operation modes and calculation of beam dynamics, measurement of the Smith-Garren curves and their recalculation into phase motion curves with the aim of evaluating the quality of magnetic fields formation and their corrections for the multi-purpose isochronous cyclotrons AIC-144 (Krakow, Poland), SC-200 (Hefei, China), DC-280 (FLNR, JINR). - Investigation of mathematical models of complex physical processes in the framework of quantum field and molecular dynamics equations. - Modeling the extremely high energy electromagnetic showers recorded in ultra-high energy neutrino astrophysics projects such as Baikal, IceCube, and Antares. - Development of methods and algorithms based on the neural network approach for solving applied problems and opening up new perspectives, including new insights into Big Data analytics.