Hierarchical Graph Networks for Accurate Weather Forecasting via Lightweight Training

TL;DR

The paper addresses the challenge of accurate long-horizon weather forecasting by modeling multiscale climate dynamics with Hierarchical Graph Neural Networks. It introduces HiFlowCast and its ensemble HiAntFlow, which couple global physics with local forecasts through Latent-Memory-Retention and Latent-to-Physics branches, and leverages pretrained components to achieve single-epoch convergence. Empirically, the Flow models outperform state-of-the-art GNN baselines, delivering consistent gains up to 13 days lead time and notable improvements for extreme events, while reducing training cost and carbon footprint. The work demonstrates practical impact by enabling more reliable, physics-informed forecasts at scale with improved efficiency, and points to future extensions with additional PDE forcings and broader datasets.

Abstract

Climate events arise from intricate, multivariate dynamics governed by global-scale drivers, profoundly impacting food, energy, and infrastructure. Yet, accurate weather prediction remains elusive due to physical processes unfolding across diverse spatio-temporal scales, which fixed-resolution methods cannot capture. Hierarchical Graph Neural Networks (HGNNs) offer a multiscale representation, but nonlinear downward mappings often erase global trends, weakening the integration of physics into forecasts. We introduce HiFlowCast and its ensemble variant HiAntFlow, HGNNs that embed physics within a multiscale prediction framework. Two innovations underpin their design: a Latent-Memory-Retention mechanism that preserves global trends during downward traversal, and a Latent-to-Physics branch that integrates PDE solution fields across diverse scales. Our Flow models cut errors by over 5% at 13-day lead times and by 5-8% under 1st and 99th quantile extremes, improving reliability for rare events. Leveraging pretrained model weights, they converge within a single epoch, reducing training cost and their carbon footprint. Such efficiency is vital as the growing scale of machine learning challenges sustainability and limits research accessibility. Code and model weights are in the supplementary materials.

Figures (8)

• Figure 1: A. Latitude–longitude grids are projected onto a periodic mesh graph, preserving global continuity. HiFlowCast and HiAntFlow load pretrained hierarchical weights. B. Both models reuse pretrained components, freezing some to stabilize training. A memory buffer retains global trends, while a physics branch injects ground-truth signals at each level, enabling multiscale forecasts.
• Figure 1: Performance comparison at 1, 10, and final lead time (13 days). Lower values indicate higher-fidelity projections. The best results are in bold, while the second best are underlined.
• Figure 2: Comparison of temperature forecasts at a 10-day lead time. HiFlowCast and HiAntFlow display high-fidelity projections over the rollout window.
• Figure 2: MAE at 13-day lead time for 1st and 99th quantile extremes. Lower is better. Gains are relative to the best non-Flow baseline.
• Figure 3: Power spectral density of projections over 8-hour and 13-day rollout windows. Proximity to the ground truth indicates how well models reproduce its detail.