• Graph neural operator surrogates population balance equations with R 2 > 0.99 across ionic strength, zeta potential, particle size, and concentration ranges • Embedding Brownian transport in graph edges achieves significant computational efficiency versus physics-informed loss while maintaining superior prediction accuracy • Attention analysis reveals model learned XDLVO-controlled regime transitions, accurately capturing collision efficiency and frequency competition effects Colloidal aggregation in natural and engineered waters is a complex function of both particle and groundwater electrochemical conditions, yet predicting aggregation behavior across diffusion-limited and reaction-limited regimes remains challenging due to the nonlinear dependence of collision efficiency on ionic strength and surface potential. This study presents a graph neural operator surrogate model that captures particle aggregation dynamics by embedding transport physics directly into the network architecture. Particle size classes are represented as graph nodes with Brownian collision kernels encoded in edge features, while attention mechanisms conditioned on ionic strength and zeta potential learn collision efficiency variations governed by extended DLVO interactions. The proposed model predicts aggregation kinetics across a range of electrochemical conditions, achieving R 2 > 0.99 for both held-out parameter combinations and temporal extrapolation, and outperforming baseline models that do not embed physics in the architecture, as well as loss-based, physics-regularized neural networks. Validation against experimental measurements from bacteriophage, polystyrene, and cerium oxide systems confirms reproduction of aggregation regime transitions and kinetic saturation. Attention analysis reveals physically consistent reorganization from multiple information pathways under strong electrostatic repulsion to integrated processing under weak repulsion. This framework enables rapid, physically grounded exploration of colloidal aggregation relevant to water quality prediction and treatment optimization.
Choe et al. (Sun,) studied this question.