Mitigating Voronoi-induced artifacts in GNN-based sea surface temperature forecasting using bathymetry-aware adaptive meshes

Accurately forecasting Sea Surface Temperature (SST) is critical for understanding ocean dynamics, climate change impacts, and marine ecosystem management (Brito-Morales et al., 2020; Gattuso et al., 2018). In recent years, Graph Neural Networks (GNNs) have emerged as a powerful tool for spatiotemporal oceanographic forecasting, offering advantages over traditional Euclidean deep learning models by operating on unstructured grids (Liang et al., 2023; Zhang et al., 2025). However, the transition from structured satellite-derived data to mesh-based representations often introduces numerical artifacts, particularly due to the grid-to-mesh coupling mechanisms (Cuervo-Londoño et al., 2026; Cuervo-Londoño, Sánchez, et al., 2025).

This study investigates the origin of "Voronoi-induced artifacts" in GNN architectures applied to SST forecasting in the Northwest African region and the Canary Islands. We demonstrate that the grid-to-mesh association is algebraically equivalent to an order-k Voronoi partition (Cuervo-Londoño, Reyes, et al., 2025; Okabe et al., 2000), implying that the way nodes are distributed and how they associate with the underlying data grid significantly influences the quality of the predictions. To address these issues, we propose and evaluate four different mesh configurations: structured quadrangular meshes (Holmberg et al., 2024; Lam et al., 2023) and three unstructured approaches, including novel bathymetry-aware meshes.

Our findings reveal that connectivity plays a decisive role in mitigating artifact formation. Specifically, using approximately four connections per node under optimized grid-to-mesh association rules significantly reduces errors. Furthermore, the results show that densifying the node distribution according to the seabed’s topography (bathymetry) not only reduce spatial artifacts but also increases forecast accuracy. The bathymetry-based meshes with optimized connectivity (3-4 connections) achieved a 30% improvement in performance compared to traditional structured mesh baselines. These insights suggest that incorporating geographical and topological priors into GNN design is essential for developing robust and reliable machine-learning surrogates for physical oceanography (Reichstein et al., 2019).

Acknowledgments: This work was supported by the projects SIRENA and SIRENA 2, funded by the collaboration of the Biodiversity Foundation of the Ministry for the Ecological Transition and the Demographic Challenge, through the Pleamar Program, and are co-financed by the European Union through the EMFAF (European Maritime, Fisheries and Aquaculture Fund).

References

Cuervo-Londoño, G. A., Reyes, J. G., Rodríguez-Santana, Á., & Sánchez, J. (2025). Voronoi-Induced Artifacts from Grid-to-Mesh Coupling and Bathymetry-Aware Meshes in Graph Neural Networks for Sea Surface Temperature Forecasting. Electronics, 14(24), 4841. https://doi.org/10.3390/electronics14244841

Cuervo-Londoño, G. A., Sánchez, J., & Rodríguez-Santana, Á. (2025). Deep Learning Weather Models for Subregional Ocean Forecasting: A Case Study on the Canary Current Upwelling System (No. arXiv:2505.24429). arXiv.https://doi.org/10.48550/arXiv.2505.24429

Cuervo-Londoño, G. A., Sánchez, J., & Rodríguez-Santana, Á. (2026). Forecasting Sea Surface Temperature from Satellite Images with Graph Neural Networks. In M. Castrillón-Santana, C. M. Travieso-González, O. Deniz Suarez, D. Freire-Obregón, D. Hernández-Sosa, J. Lorenzo-Navarro, & O. J. Santana (Eds.), Computer Analysis of Images and Patterns (pp. 329–339). Springer Nature Switzerland. https://doi.org/10.1007/978-3-032-05060-1_28