Physics-informed neural networks for aggregation kinetics

Abstract We introduce a physics-informed method for finding numerical solutions of large systems of equations governing aggregation kinetics. The method enables accurate reconstruction of density distributions for both large and small clusters, with notable improvements for small cluster sizes, as compared to previous numerical approaches. The efficiency and accuracy are improved by restricting the physics-informed loss to a small interval, enabling long time horizons with minimal extra computational cost. The superiority of the method has been demonstrated for basic aggregation kernels – constant, additive, multiplicative and generalised Brownian kernel, showing that one simple neural architecture can be used for four distinct kernels. In addition to numerical examples, we provide rigorous mathematical justification for the approach and derive relevant analytical error bounds. Combined high efficiency and low error margins of the method indicate strong potential for long-term prediction and integration into broader computational systems.