{"title":"Application of machine learning technique for a fast forecast of aggregation kinetics in space-inhomogeneous systems","authors":"","doi":"10.1016/j.physa.2024.130032","DOIUrl":null,"url":null,"abstract":"<div><p>Modelling 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 the particle propagation could be done in parallel. Yet the numerics with many aggregate sizes remains quite resource-demanding. Here, we explore the way to reduce the amount of direct computations by replacing the actual numerical solution of the Smoluchowski equations with the respective density transformations learned with the application of one of machine learning (ML) methods, the conditional normalising flow. We demonstrate that the ML predictions for the space distribution of aggregates and their size distribution require drastically shorter computation time and agree 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 fast (on the timescale of data reading) prediction and visualisation of pollution processes, providing a tool with a reasonable trade off between the prediction accuracy and the computational time.</p></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica A: Statistical Mechanics and its Applications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378437124005417","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Modelling 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 the particle propagation could be done in parallel. Yet the numerics with many aggregate sizes remains quite resource-demanding. Here, we explore the way to reduce the amount of direct computations by replacing the actual numerical solution of the Smoluchowski equations with the respective density transformations learned with the application of one of machine learning (ML) methods, the conditional normalising flow. We demonstrate that the ML predictions for the space distribution of aggregates and their size distribution require drastically shorter computation time and agree 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 fast (on the timescale of data reading) prediction and visualisation of pollution processes, providing a tool with a reasonable trade off between the prediction accuracy and the computational time.
期刊介绍:
Physica A: Statistical Mechanics and its Applications
Recognized by the European Physical Society
Physica A publishes research in the field of statistical mechanics and its applications.
Statistical mechanics sets out to explain the behaviour of macroscopic systems by studying the statistical properties of their microscopic constituents.
Applications of the techniques of statistical mechanics are widespread, and include: applications to physical systems such as solids, liquids and gases; applications to chemical and biological systems (colloids, interfaces, complex fluids, polymers and biopolymers, cell physics); and other interdisciplinary applications to for instance biological, economical and sociological systems.