PhD Research Seminar: Machine Learning and Graph Analysis, Systems of Equations and Multicomponent Gas Mixture

First talk: Machine Learning for Graph Analysis    
Speaker: Sergey Slashchinin, second-year PhD student, HSE Nizhny Novgorod

Machine learning has been successfully used in various areas, such as computer vision and natural language processing, especially with the phenomenal boost in effectiveness from deep learning models. Right now, many studies are focused on extending deep learning methods to different types of data, for example, graph structures. Usually graph analysis involves solving some combinatorial optimization problems, which can be hard for traditional solvers. Recent successful attempts at leveraging deep learning to solve combinatorial optimization problems will be discussed.

Second talk: On Properties of Aggregated Regularized Systems of Equations for a Homogeneous Multicomponent Gas Mixture     
Speaker: Anna Fedchenko, second-year PhD student, Faculty of Economic Sciences

Most of gaseous substances that are found in nature and used in industrial workflows are mixtures of different gases. Regularized quasi-gasdynamic (QGD) and quasi-hydrodynamic (QHD) systems of equations have been used for several decades in computer simulation of a broad variety of gas dynamics problems. These systems of equations are suitable for discretization and construction of simple and fairly effective explicit mesh methods, and QGD and QHD systems are successfully applied to model flows at, respectively, any and moderate Mach numbers.

During the talk, the speaker will present two aggregated regularized systems of equations for a multicomponent homogeneous gas mixture and discuss some of their properties. First of all, an entropy balance equation with a non-negative entropy production was derived for them in the presence of diffusion fluxes. The existence, uniqueness, and L²-dissipativity of weak solutions to an initial-boundary value problem for the systems linearized on a constant solution were established. The Petrovskii parabolicity and the local in time classical unique solvability of the Cauchy problem were also proved for the aggregated systems themselves.