Computer modeling and numerical-analytical research methods of complex physicotechnical systems and infocommunication (information and communications) technologies.

• Symbolic-numerical solution of problems in quantum physics and wave optics, automation of the processing of experimental data obtained using accelerators, numerical computation of stochastic dynamics problems.
• Enhancement of functional models for optical and quantum-physical devices based on wave optical and quantum-mechanical effects; Modification of continuous numerical computation for solving direct problems of simulation of waveguide propagation of electromagnetic radiation in integrated optical waveguides, diffraction of polarized monochromatic electromagnetic radiation on subwave optical grating and evolution of small-size quantum mechanical systems.
• Computer implementation of symbolic numerical algorithms for solving initial boundary problems for corresponding systems of partial differential equations and studying their stability-like and symmetry properties.
• Development of research techniques for Markov and single-step processes; enhancement of research techniques for stochastic and statistic processes.
• Computer implementation of analytical and numerical algorithms for solving initial boundary value problems for the corresponding systems of partial differential equations, stochastic differential equations, integro-partial differential equations.

• Study of Hamilton action construction for various types of motion equations of infinite-dimensional systems and representability of equations in the form of Euler-Lagrange equations with nonpotential force densities, Hamilton equations and Hamilton admissible equations.

• Creation of information technology in the form of complex methods for managing radio resources in heterogeneous 5G wireless networks that support Internet of Things technologies.

The main goal of the Project is to create a practical center at the international level to improve computational methods for applied problems in mathematical physics. Currently, the Center's employees are focused on the implementation of symbolic-numerical algorithms for solving problems in quantum physics and wave optics as well as automated processing of experimental data obtained from accelerators.

The Center develops, approbates, and enhances computer data processing methods together with colleagues from the Laboratory of Information Technologies at the Joint Institute for Nuclear Research (JINR). The development, approbation, and improvement of symbolic-numerical algorithms for solving quantum physics problems are conducted together with colleagues from the Laboratory of Theoretical Physics at JINR. The work on the study of numerical computations of stochastic dynamics problems is carried out together with employees from the International Scientific Center at JINR, Jozef Šafárik Slovak University, the Federal Research Center “Informatics and Management”, and the M.V. Keldysh Institute of Applied Mathematics.