# Njord: A Probabilistic Graph Neural Network for Ensemble Ocean Forecasting

arXiv: https://arxiv.org/abs/2605.15470 · HTML: https://mlsanity.com/paper/2605.15470/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 46 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 7 of 7)

- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [Skillful joint probabilistic weather forecasting from marginals](https://mlsanity.com/paper/2506.10772/) (2025)
- [FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale](https://mlsanity.com/paper/2507.12144/) (2025)
- [Coupled Ocean-Atmosphere Dynamics in a Machine Learning Earth System Model](https://mlsanity.com/paper/2406.08632/) (2024)
- [Building Machine Learning Limited Area Models: Kilometer-Scale Weather Forecasting in Realistic Settings](https://mlsanity.com/paper/2504.09340/) (2025)
- [High-Resolution Probabilistic Data-Driven Weather Modeling with a Stretched-Grid](https://mlsanity.com/paper/2511.23043/) (2025)
- [Data-driven ensemble prediction of the global ocean](https://mlsanity.com/paper/2603.19591/) (2026)

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

- [HClimRep-Ocean: A Global Ocean Emulator on an Unstructured Mesh](https://mlsanity.com/paper/2609.28601/) (2026)

## Abstract (arXiv)

Ocean dynamics are inherently chaotic, yet existing machine learning ocean models produce only deterministic forecasts. We introduce Njord, a probabilistic data-driven model for ocean forecasting, applicable to both global and regional domains. Njord combines a deep latent variable framework with a graph neural network architecture, enabling sampling each forecast step in a single forward pass. We apply Njord globally at 0.25deg resolution and regionally to the Baltic Sea at 2 km resolution. To scale to these large ocean grids we introduce K-means cluster meshes that adapt to irregular sea surface geometry. Experiments demonstrate strong performance on both domains compared to deterministic machine learning baselines, while also providing uncertainty estimates from the sampled ensemble forecasts. On the global OceanBench benchmark, Njord achieves the lowest errors on average across upper-ocean variables when evaluated against real-world observations, with the largest improvements in surface temperature prediction.