George Ovchinnikov

Alexandr Katrutsa, Mike Botchev, George Ovchinnikov et al.

The conjugate gradient method (CG) is typically used with a preconditioner which improves efficiency and robustness of the method. Many preconditioners include parameters and a proper choice of a preconditioner and its parameters is often not a trivial task. Although many convergence estimates exist which can be used for optimizing preconditioners, these estimates typically hold for all initial guess vectors, in other words, they reflect the worst convergence rate. To account for the mean convergence rate instead, in this paper, we follow a stochastic approach. It is based on trial runs with random initial guess vectors and leads to a functional which can be used to monitor convergence and to optimize preconditioner parameters in CG. Presented numerical experiments show that optimization of this new functional with respect to preconditioner parameters usually yields a better parameter value than optimization of the functional based on the spectral condition number.

Filipp Skomorokhov, George Ovchinnikov

This paper is dedicated to the application of reinforcement learning combined with neural networks to the general formulation of user scheduling problem. Our simulator resembles real world problems by means of stochastic changes in environment. We applied Q-learning based method to the number of dynamic simulations and outperformed analytical greedy-based solution in terms of total reward, the aim of which is to get the lowest possible penalty throughout simulation.

Artem Chashchin, Mikhail Botchev, Ivan Oseledets et al.

Forecasting time series and time-dependent data is a common problem in many applications. One typical example is solving ordinary differential equation (ODE) systems $\dot{x}=F(x)$. Oftentimes the right hand side function $F(x)$ is not known explicitly and the ODE system is described by solution samples taken at some time points. Hence, ODE solvers cannot be used. In this paper, a data-driven approach to learning the evolution of dynamical systems is considered. We show how by training neural networks with ResNet-like architecture on the solution samples, models can be developed to predict the ODE system solution further in time. By evaluating the proposed approaches on three test ODE systems, we demonstrate that the neural network models are able to reproduce the main dynamics of the systems qualitatively well. Moreover, the predicted solution remains stable for much longer times than for other currently known models.