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Mesh Interpolation Graph Network for Dynamic and Spatially Irregular Global Weather Forecasting

NeurIPS 2025 · Graph learning › Knowledge and temporal graphs · approach: Continuous-time dynamic graph learning · 1 citations (OpenAlex)

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Proposes MIGN, a graph network that maps irregular weather station observations onto a regular HEALPix mesh via message passing and uses learnable parametric spherical harmonics location embeddings, enabling global station forecasting and generalization to unseen stations on NOAA GSOD data.

Problem

Global weather station forecasting where stations are spatially irregular and their number and locations change over time, requiring generalization to unobserved locations.

Approach

Encode irregular station observations onto a regular HEALPix mesh through a learned station-to-mesh message passing (an interpolation analogue), process on the mesh, decode back to stations, and represent location with learnable real spherical harmonic coefficients concatenated to node features instead of raw coordinates.

Key results

• MIGN reduces MSE by about 13% on MAX TEMP, 15% on MIN TEMP and 15% on DEWP/SLP versus the strongest baseline in the 1-day setting (e.g., MAX TEMP 8.47 vs 9.74 for STGCN).
• In the unseen-station global generalization test, MIGN achieves MSE 8.55 on MAX TEMP and 8.05 on MIN TEMP, versus 9.81 and 9.52 for the closest baselines.
• Ablation shows mesh interpolation and spherical harmonics embedding each improve results; SH embedding outperforms direct coordinate, WRAP and Cartesian 3D embeddings on all six variables.

Measured effects reported in the paper

Surprising findings

• A coordinate-free-free comparison: a Pangu 0.25° gridded forecast interpolated to stations performs worse than MIGN on MAX and MIN TEMP in the station-based comparison, although in the unmonitored-location test Pangu at 0.25° outperforms MIGN on MAX TEMP (11.45 vs 13.84).

Limitations

• Only land-based stations are used because marine station coverage is sparse, so ocean regions are not modeled.
• Station-based models can only predict at locations with observation data, leaving remote oceans, deserts and polar areas unmodeled.
• Evaluation is restricted to a single daily dataset (NOAA GSOD) and six variables.

Experimental setup

Datasets: NOAA GSOD

Benchmarks: NOAA GSOD

Metrics: MSE MAE

Baselines: STGCN MPNNLSTM DualCast T&S-IMP T&S-AMP TTS-IMP TTS-AMP DyGrAE ReDyNet HD-TTS STAR GTN

Builds on: GraphCast HEALPix Geographic Location Encoder GINO

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