Application of machine learning technique for a fast forecast of aggregation kinetics in space-inhomogeneous systems
This provides a faster forecasting tool for space-dependent particle size distributions, with practical applications such as online prediction of pollution processes, though it is incremental as it builds on existing low-rank approximations and parallel methods.
The paper tackled the computationally intensive problem of modeling aggregation kinetics in space-inhomogeneous systems by replacing direct numerical solutions of Smoluchowski equations with machine learning predictions using conditional normalizing flows, resulting in drastically reduced computation time while maintaining fair agreement with simulations.
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.