Unstructured mesh-based graph neural networks for estimating the spatiotemporal distribution of a human-induced chemical in freshwater

• A mesh-based GNN is proposed to estimate anthropogenic chemical concentrations. • Input data include physics-based model outputs, observations, and estimations. • Spatiotemporal dataset division significantly affects the Mesh-GNN model performance. • Message-passing step and hidden dimension are key hyperparameters. • Our model efficiently maps acesulfame, preserving a detailed triangular mesh. Artificial sweeteners such as acesulfame are anthropogenic contaminants increasingly detected in natural waters via wastewater effluents. Numerical models such as HydroGeoSphere (HGS) are widely used to simulate their spatiotemporal transport. However, high computational demands—especially when using unstructured meshes to capture complex geometries—limit their scalability for large-scale or long-term applications. To address this limitation, we developed a mesh-based graph neural network (Mesh-GNN), adapted from MeshGraphNets, to efficiently emulate HGS outputs over unstructured triangular meshes. The model was applied to the upper Grand River, Ontario, Canada, using topographical, geographical, hydrological, hydrometeorological, and wastewater point-source data to estimate acesulfame concentrations. Mesh-GNN retained the node and edge structure of the HGS mesh and enabled rapid inference via message passing. The model training yielded Nash-Sutcliffe Efficiency (NSE) values of 0.93 (spatial split) and 0.86 (temporal split), with corresponding validation NSEs of 0.69 and 0.70. Incorporating field observations with HGS-simulated concentrations improved accuracy at sampling sites by up to 29.7% compared to HGS alone. While HGS solves nonlinear partial differential equations across a three-dimensional watershed-scale mesh (∼3.5 million nodes), requiring several days per simulation, Mesh-GNN operates on a simplified two-dimensional upstream segment (5,755 nodes), enabling inference within seconds. These findings highlight the potential of Mesh-GNN-based surrogate models for efficient and scalable water quality prediction.