Unstructured Mesh-Based Graph Neural Networks for Estimating the Spatiotemporal Distribution of a Human-Induced Chemical in Freshwater

Abstract

Artificial sweeteners, such as acesulfame, are human-induced chemicals increasingly detected in natural water bodies via wastewater effluents. Numerical models, including HydroGeoSphere (HGS), stimulate their spatiotemporal distributions and monitor anthropogenic impacts on water systems. The accuracy and computational demands of these simulations depend on mesh discretization. Unstructured meshes offer greater flexibility for complex geometries than structured rectangular ones, although they incur higher computational costs. To address this, we developed a mesh-based graph neural network (Mesh-GNN) based on MeshGraphNets to process unstructured triangular meshes, optimizing both accuracy and computational efficiency. This model replicated HGS outputs to estimate spatiotemporal concentrations of acesulfame in the upper Grand River, Ontario, Canada, using topographical, geographical, hydrological, hydrometeorological, and wastewater point-source data. The Mesh-GNN model retained nodes, edges, and spatial relationships from the HGS model unstructured mesh, achieving validation coefficient of determination (R2) values of 0.73 and 0.75 for spatially and temporally split datasets, respectively. Our data-assemblage approach, combining HGS-simulated and field-sampled acesulfame concentrations, improved accuracy by up to 29.7% at sampling sites compared to HGS estimates alone. These findings support applications in water resource management and human impact assessment.

Keywords: MeshGraphNet, Unstructured triangular mesh, Artificial Sweetener, HydroGeoSphere