Department of mathematical modeling

The development and implementation of artificial intelligence systems is an integral part of the development of modern control systems and a wide range of intelligent equipment. Based on the deep learning of neural networks, artificial intelligence is an important addition to the means and tools of classical mathematical modeling.

In the new millennium, machine learning, as a science that studies the problems of analysis, processing and presentation of data in digital form, is the mainstream of digital and computer technologies. And since this field is developing by leaps and bounds, professionals began to use the terms “weak artificial intelligence” and “strong artificial intelligence” more and more often. The first refers to systems that learn and are able to solve individual tasks, and the second refers to intelligent systems capable of intellectual thinking and establishing cause-and-effect relationships based on the processing of various data. Thus, machine learning makes it possible to turn a robot into an analyst, able to build a forecast for a given value based on regularities or analyze and adjust the effectiveness of the applied treatment method, the distribution of logistics flows, the workload of production lines, detect errors in technology, etc.

Quantum computing is a strategic interest of future technological development. They allow, by their very nature, parallel computation of incredibly complex specific tasks, which are simply beyond the power of existing (and future) classic supercomputers.

An important direction is the mathematical modeling and research of non-stationary physical processes of 3D printing by the method of selective laser melting (SLM) for the manufacture of technical elements from titanium and heat-resistant alloys.

As research methods, theoretical approaches are used, which are based on the solution of the system of non-stationary nonlinear differential equations of mathematical physics, which describe the processes of heat and mass transfer and hydrodynamics.

The goal of the scientific direction is the development of specialized software and methodological support (CFD code) for modeling non-stationary physical processes during selective laser melting of metal powders. This will make it possible to gain a deeper understanding of the physics of the phenomenon, to provide recommendations on rational modes of operation of specialized equipment, as well as to improve the technology of 3D printing by the method of selective laser melting for the manufacture of elements of military equipment from titanium and heat-resistant alloys.

Numerical reconstruction of non-stationary processes is carried out by solving the Navier-Stokes equations, heat transfer and the equation describing the movement of the free surface. The specialized CFD code under development will allow to effectively and flexibly achieve the required level of compromise between computational resources and the quality of results. Numerical and experimental studies will be conducted to study the physical phenomena occurring during the selective laser melting of metal powders .

The developed model will allow a better understanding of the physics of the VLP process and reproduce real physical phenomena in a wide range of process parameters. Thus, it will accelerate the development of process parameters for new materials and increase the reliability of the process and manufactured components. As a result, new technical ideas will be formulated, physically justified modifications of the constructions of VLP-equipment will be proposed, as well as recommendations will be provided regarding their operation modes in order to ensure high efficiency values.