# Advancing Parsimonious Deep Learning Weather Prediction using the HEALPix Mesh

arXiv: https://arxiv.org/abs/2311.06253 · HTML: https://mlsanity.com/paper/2311.06253/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 70 references that are in the map.
- First posted on arXiv 11 Sep 2023.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [UNet 3+: A Full-Scale Connected UNet for Medical Image Segmentation](https://mlsanity.com/paper/2004.08790/) (2020)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [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)
- [FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2208.05419/) (2022)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Delving Deeper into Convolutional Networks for Learning Video Representations](https://mlsanity.com/paper/1511.06432/) (2015)
- [Improving data-driven global weather prediction using deep convolutional neural networks on a cubed sphere](https://mlsanity.com/paper/2003.11927/) (2020)
- [Sub-seasonal forecasting with a large ensemble of deep-learning weather prediction models](https://mlsanity.com/paper/2102.05107/) (2021)
- [DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications](https://mlsanity.com/paper/1810.12186/) (2018)
- [SwinVRNN: A Data-Driven Ensemble Forecasting Model via Learned Distribution Perturbation](https://mlsanity.com/paper/2205.13158/) (2022)
- [Global Extreme Heat Forecasting Using Neural Weather Models](https://mlsanity.com/paper/2205.10972/) (2022)
- [CIRA Guide to Custom Loss Functions for Neural Networks in Environmental Sciences -- Version 1](https://mlsanity.com/paper/2106.09757/) (2021)

## Built on by (most cited first, 28 of 28)

- [ACE2: Accurately learning subseasonal to decadal atmospheric variability and forced responses](https://mlsanity.com/paper/2411.11268/) (2024)
- [LUCIE: A Lightweight Uncoupled ClImate Emulator with long-term stability and physical consistency for O(1000)-member ensembles](https://mlsanity.com/paper/2405.16297/) (2024)
- [Samudra: An AI Global Ocean Emulator for Climate](https://mlsanity.com/paper/2412.03795/) (2024)
- [Coupled Ocean-Atmosphere Dynamics in a Machine Learning Earth System Model](https://mlsanity.com/paper/2406.08632/) (2024)
- [Huge Ensembles Part I: Design of Ensemble Weather Forecasts using Spherical Fourier Neural Operators](https://mlsanity.com/paper/2408.03100/) (2024)
- [Analyzing and Exploring Training Recipes for Large-Scale Transformer-Based Weather Prediction](https://mlsanity.com/paper/2404.19630/) (2024)
- [U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecaster](https://mlsanity.com/paper/2604.09041/) (2026)
- [Attention on the Sphere](https://mlsanity.com/paper/2505.11157/) (2025)
- [EnScale: Temporally-consistent multivariate generative downscaling via proper scoring rules](https://mlsanity.com/paper/2509.26258/) (2025)
- [Atmospheric Predictability Beyond 30 Days with Machine Learning](https://mlsanity.com/paper/2504.20238/) (2025)
- [PEAR: Equal Area Weather Forecasting on the Sphere](https://mlsanity.com/paper/2505.17720/) (2025)
- [Causal Climate Emulation with Bayesian Filtering](https://mlsanity.com/paper/2506.09891/) (2025)
- [(Sparse) Attention to the Details: Preserving Spectral Fidelity in ML-based Weather Forecasting Models](https://mlsanity.com/paper/2604.16429/) (2026)
- [Community Research Earth Digital Intelligence Twin (CREDIT)](https://mlsanity.com/paper/2411.07814/) (2024)
- [BeamVQ: Beam Search with Vector Quantization to Mitigate Data Scarcity in Physical Spatiotemporal Forecasting](https://mlsanity.com/paper/2502.18925/) (2025)
- [Can AI Weather Models Predict Beyond Two Weeks? A Quantitative Benchmark and Analysis of Long Rollouts](https://mlsanity.com/paper/2605.30184/) (2026)
- [Score-based generative emulation of impact-relevant Earth system model outputs](https://mlsanity.com/paper/2510.04358/) (2025)
- [MoWE : A Mixture of Weather Experts](https://mlsanity.com/paper/2509.09052/) (2025)
- [Examining Fast Radiatively Driven Responses Using Machine-Learning Weather Emulators](https://mlsanity.com/paper/2602.16090/) (2026)
- [Exploring Design Choices for Autoregressive Deep Learning Climate Models](https://mlsanity.com/paper/2505.02506/) (2025)
- [Crowdsourcing the Frontier: Advancing Hybrid Physics-ML Climate Simulation via a 50,000 Kaggle Competition](https://mlsanity.com/paper/2511.20963/) (2025)
- [On the importance of learning non-local dynamics for stable data-driven climate modeling: A 1D gravity wave-QBO testbed](https://mlsanity.com/paper/2407.05224/) (2024)
- [AtmosMJ: Revisiting Gating Mechanism for AI Weather Forecasting Beyond the Year Scale](https://mlsanity.com/paper/2506.09733/) (2025)
- [Searth Transformer: A Transformer Architecture Incorporating Earth's Geospheric Physical Priors for Global Mid-Range Weather Forecasting](https://mlsanity.com/paper/2601.09467/) (2026)
- [Scaling Storm-Resolving Atmospheric AI Simulation to the Entire Planet](https://mlsanity.com/paper/2606.31248/) (2026)
- [Rescene: band-limited stochastic forcing turns a frozen neural weather operator into a climate emulator](https://mlsanity.com/paper/2608.09971/) (2026)
- [Learning Hierarchical Causal Representations of the Effects of Forcings on Temperature in Climate Models](https://mlsanity.com/paper/2609.30995/) (2026)
- [S3N: A Spherical Spiral Scanning Network for Weather Forecasting](https://mlsanity.com/paper/2610.04338/) (2026)

## Abstract (arXiv)

We present a parsimonious deep learning weather prediction model to forecast seven atmospheric variables with 3-h time resolution for up to one-year lead times on a 110-km global mesh using the Hierarchical Equal Area isoLatitude Pixelization (HEALPix). In comparison to state-of-the-art (SOTA) machine learning (ML) weather forecast models, such as Pangu-Weather and GraphCast, our DLWP-HPX model uses coarser resolution and far fewer prognostic variables. Yet, at one-week lead times, its skill is only about one day behind both SOTA ML forecast models and the SOTA numerical weather prediction model from the European Centre for Medium-Range Weather Forecasts. We report several improvements in model design, including switching from the cubed sphere to the HEALPix mesh, inverting the channel depth of the U-Net, and introducing gated recurrent units (GRU) on each level of the U-Net hierarchy. The consistent east-west orientation of all cells on the HEALPix mesh facilitates the development of location-invariant convolution kernels that successfully propagate weather patterns across the globe without requiring separate kernels for the polar and equatorial faces of the cube sphere. Without any loss of spectral power after the first two days, the model can be unrolled autoregressively for hundreds of steps into the future to generate realistic states of the atmosphere that respect seasonal trends, as showcased in one-year simulations.