GNADET: A geospatial neural advection–diffusion equation framework with graph transformer for surface temperature forecasting

Abstract Accurate surface temperature forecasting is essential for climate change research, yet achieving both high predictive accuracy and physical consistency remains a persistent challenge. Purely data-driven machine learning models often lack physical interpretability and can struggle with generalization, sometimes producing physically implausible results. Therefore, this study introduces the Geospatial Neural Advection–Diffusion Equation with Graph Transformer called GNADET, which is a novel hybrid forecasting framework for surface temperature. The core of GNADET is a physics-informed neural ordinary differential equation that embeds the advection–diffusion equation to model physical dynamics. By representing gridded geospatial data as a graph based on the Moore neighborhood, a Graph Transformer is employed to learn and compensate for complex, spatially-correlated uncertainties that the explicit physics cannot account for. All components of the framework are trained jointly, which allows the model to learn complex data patterns while being constrained by physical principles. This study evaluates GNADET using the WeatherBench ERA5 dataset on a global scale and across several diverse continents. The framework shows high predictive accuracy and strong generalization when being extrapolated to new times and locations, outperforming comparative models. By integrating physics-informed and data-driven techniques, GNADET provides an accurate and interpretable solution for large-scale surface temperature forecasting.