Mesh Interpolation Graph Networks for Spatially Irregular Global Weather Forecasting
Forecasting weather on a truly global scale is a delicate balance between physics-based fidelity and the messiness of real-world geography. Oceans, mountains, coastlines, and uneven sensor coverage create spatial irregularities that traditional grids struggle to capture. Mesh interpolation graph networks offer a compelling alternative: they combine geometric representation with graph learning to forecast in a world that doesn’t fit neatly onto a square lattice.
Why a Mesh? Rethinking Spatial Representation
Regular grids impose a uniform spacing that underserves coastal regions and terrain boundaries. A mesh, by contrast, adapts resolution where it matters most, creating finer detail near landforms and data-dense zones while keeping a coarser volume over vast open oceans. In this setup, nodes carry physical state information—temperature, pressure, humidity, wind vectors—while edges encode adjacency and physical relationships, such as heat exchange or moisture transport. The result is a representation that mirrors the planet’s geometry and observational realities, enabling more faithful propagation of atmospheric signals across irregular boundaries.
- Adaptive resolution aligns data fidelity with geography and observation density
- Natural handling of coastlines, terrain, and sea-ice boundaries
- Seamless data fusion across multimodal sources, from satellites to drifting buoys
Key Ingredients: Mesh Construction, Interpolation, and Dynamics
A typical pipeline starts with constructing a geospatial mesh that respects physical geography and data availability. Node features capture instantaneous state variables, while edge types encode directional connections and physical processes. A graph neural network then propagates information through the mesh, learning how local interactions accumulate into regional patterns. An interpolation module maps between the irregular mesh and conventional forecast grids, enabling assimilation, visualization, and comparison with legacy models.
- Mesh generation strategies: geodesic, Delaunay, or Voronoi schemes tuned to coastlines and topography
- Feature embedding: temperature, pressure, humidity, wind speed and direction, cloud fraction
- Interpolation as a learning bridge: preserves spatial coherence when moving between resolutions
- Temporal dynamics: incorporating recurrent or temporal graph components to capture diurnal and synoptic cycles
The interpolation step is not a mere resampling—it’s a learning-enabled bridge that preserves spatial coherence across irregular boundaries.
Dynamic and Spatially Irregular Graphs: Why It Matters
Global weather is not static, and neither should be the graph that models it. The topology can evolve as new observations arrive, sensor availability shifts, or as we refine coastal and land-sea masks. A dynamic graph allows edges to be added, removed, or reweighted, enabling the model to adapt to changing data landscapes while maintaining temporal consistency across forecasts.
- Edge updates reflect changing observational coverage and physical connectivity
- Temporal consistency helps suppress spurious fluctuations at region boundaries
Performance, Evaluation, and Real-World Impact
Evaluating mesh-based forecasts involves standard metrics such as RMSE and MAE, but also probabilistic scores like CRPS to account for forecast uncertainty. Regional analyses show notable improvements near coastlines, high-relief terrain, and zones with sparse observations, where irregular meshes can allocate more representational capacity. Cross-validation across historical storm events and seasonal cycles demonstrates the value of learning-based interpolation in capturing abrupt fronts and moisture advection.
In field tests, mesh-interpolated forecasts delivered sharper fronts and better precipitation timing around complex coastlines compared with uniform grids.
Challenges on the Horizon
- Scalability: global graphs at high resolution demand efficient architectures and possibly hierarchical meshes
- Data assimilation: integrating observations directly on irregular meshes remains technically intricate
- Uncertainty quantification: calibrating and communicating predictive intervals on nonuniform grids
- Workflow integration: aligning mesh-based forecasts with current NWP pipelines and operational constraints
Practical Takeaways for Researchers and Practitioners
Flexibility pays off: modular mesh design and interpolation losses let teams tailor models to regional priorities and compute budgets. Start with coastal or island-heavy domains to validate benefits before scaling globally.
Operationally, a mesh interpolation graph network can serve as a complementary component to traditional NWP, offering enhanced fidelity where data gaps and geographic complexity traditionally degrade performance. The key is to balance resolution with computational cost, while preserving physical interpretability through transparent edge definitions and physics-inspired loss terms.
Looking Ahead
As researchers push toward end-to-end trainable systems that respect geophysical constraints, mesh interpolation graph networks stand out as a principled path for spatially irregular forecasting. By weaving together adaptive geometry, learned propagation, and robust interpolation, this approach holds promise for more accurate, geographically aware weather predictions—especially in the regions that matter most for societies and ecosystems.