R. R. Zagidullin

M. A. Larchenko, R. R. Zagidullin, V. V. Palyulin et al.

Modeling of aggregation processes in space-inhomogeneous systems is extremely numerically challenging since complicated aggregation equations -- Smoluchowski equations are to be solved at each space point along with the computation of particle propagation. Low rank approximation for the aggregation kernels can significantly speed up the solution of Smoluchowski equations, while particle propagation could be done in parallel. Yet the simulations with many aggregate sizes remain quite resource-demanding. Here, we explore the way to reduce the amount of direct computations with the use of modern machine learning (ML) techniques. Namely, we propose to replace the actual numerical solution of the Smoluchowki equations with the respective density transformations learned with the application of the conditional normalising flow. We demonstrate that the ML predictions for the space distribution of aggregates and their size distribution requires drastically less computation time and agrees fairly well with the results of direct numerical simulations. Such an opportunity of a quick forecast of space-dependent particle size distribution could be important in practice, especially for the online prediction and visualisation of pollution processes, providing a tool with a reasonable tradeoff between the prediction accuracy and the computational time.

Nikolay Kalmykov, Rishat Zagidullin, Oleg Rogov et al.

Modulation instability is a phenomenon of spontaneous pattern formation in nonlinear media, oftentimes leading to an unpredictable behaviour and a degradation of a signal of interest. We propose an approach based on reinforcement learning to suppress the unstable modes by optimizing the parameters for the time modulation of the potential in the nonlinear system. We test our approach in 1D and 2D cases and propose a new class of physically-meaningful reward functions to guarantee tamed instability.