# Hierarchical Graph Networks for Accurate Weather Forecasting via Lightweight Training

arXiv: https://arxiv.org/abs/2510.22094 · HTML: https://mlsanity.com/paper/2510.22094/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 54 references that are in the map.
- First posted on arXiv 25 Oct 2025.

## Builds on (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Carbon Emissions and Large Neural Network Training](https://mlsanity.com/paper/2104.10350/) (2021)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [Estimating the Carbon Footprint of BLOOM, a 176B Parameter Language Model](https://mlsanity.com/paper/2211.02001/) (2022)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [The Carbon Footprint of Machine Learning Training Will Plateau, Then Shrink](https://mlsanity.com/paper/2204.05149/) (2022)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis](https://mlsanity.com/paper/2410.16032/) (2024)
- [Hierarchical Graph Pooling with Structure Learning](https://mlsanity.com/paper/1911.05954/) (2019)
- [LLMCarbon: Modeling the end-to-end Carbon Footprint of Large Language Models](https://mlsanity.com/paper/2309.14393/) (2023)
- [A Review of Graph Neural Networks and Their Applications in Power Systems](https://mlsanity.com/paper/2101.10025/) (2021)
- [Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations](https://mlsanity.com/paper/1709.00037/) (2017)
- [Probabilistic Weather Forecasting with Hierarchical Graph Neural Networks](https://mlsanity.com/paper/2406.04759/) (2024)
- [Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting](https://mlsanity.com/paper/2305.19183/) (2023)

## Built on by (most cited first, 1 of 1)

- [Forecasting Is Not Attribution: Localizing Decoder Bypass in Graph-Based Neural Marketing Mix Models](https://mlsanity.com/paper/2606.12687/) (2026)

## Abstract (arXiv)

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.