Data-Driven Approach for Modeling Coagulation Kinetics

Two approaches for the data-driven modeling of aggregation kinetics, described by Smoluchowski equations, are analyzed for binary and ternary coagulation. The first approach uses the dynamic mode decomposition (DMD) and the second one is based on the artificial neural networks (ANN). We obtain the numerical solution of the Smoluchowski equations and compare it with the predictions yielding by DMD and ANN methods. To construct the forecast for the solution, the initial stage of the system evolution was used. We demonstrate that the DMD approach can accurately predict the size distribution of the aggregates up to the time, five times larger than the training time. In contrast, the straightforward application of the ANN approach fails to provide an accurate forecast. Hence we conclude that the DMD approach is an effective tool for modeling aggregation kinetics, even for complex aggregation events. At the same time the application of the ANN approach requires its further adaptation for the studied system, perhaps by implementation of physically-informed ANN and specially tailored loss functions.