# Ensemble Graph Neural Networks for Probabilistic Sea Surface Temperature Forecasting via Input Perturbations

arXiv: https://arxiv.org/abs/2603.06153 · HTML: https://mlsanity.com/paper/2603.06153/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 6 Mar 2026.

## Builds on (most cited first, 18 of 18)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [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)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [A Survey on Ensemble Learning under the Era of Deep Learning](https://mlsanity.com/paper/2101.08387/) (2021)
- [ArchesWeather & ArchesWeatherGen: a deterministic and generative model for efficient ML weather forecasting](https://mlsanity.com/paper/2412.12971/) (2024)
- [Probabilistic Weather Forecasting with Hierarchical Graph Neural Networks](https://mlsanity.com/paper/2406.04759/) (2024)
- [Graph-based Neural Weather Prediction for Limited Area Modeling](https://mlsanity.com/paper/2309.17370/) (2023)
- [GNN-Ensemble: Towards Random Decision Graph Neural Networks](https://mlsanity.com/paper/2303.11376/) (2023)
- [Ensemble Learning for Graph Neural Networks](https://mlsanity.com/paper/2310.14166/) (2023)
- [Deep Learning Weather Models for Subregional Ocean Forecasting: A Case Study on the Canary Current Upwelling System](https://mlsanity.com/paper/2505.24429/) (2025)
- [Leveraging an Atmospheric Foundational Model for Subregional Sea Surface Temperature Forecasting](https://mlsanity.com/paper/2510.25563/) (2025)

## Abstract (arXiv)

Accurate regional ocean forecasting requires models that are both computationally efficient and capable of representing predictive uncertainty. This work investigates ensemble learning strategies for sea surface temperature (SST) forecasting using Graph Neural Networks (GNNs), with a focus on how input perturbation design affects forecast skill and uncertainty representation. We adapt a GNN architecture to the Canary Islands region in the North Atlantic and implement a homogeneous ensemble approach inspired by bagging, where diversity is introduced during inference by perturbing initial ocean states rather than retraining multiple models. Several noise-based ensemble generation strategies are evaluated, including Gaussian noise, Perlin noise, and fractal Perlin noise, with systematic variation of noise intensity and spatial structure. Ensemble forecasts are assessed over a 15-day horizon using deterministic metrics (RMSE and bias) and probabilistic metrics, including the Continuous Ranked Probability Score (CRPS) and the Spread-skill ratio. Results show that, while deterministic skill remains comparable to the single-model forecast, the type and structure of input perturbations strongly influence uncertainty representation, particularly at longer lead times. Ensembles generated with spatially coherent perturbations, such as low-resolution Perlin noise, achieve better calibration and lower CRPS than purely random Gaussian perturbations. These findings highlight the critical role of noise structure and scale in ensemble GNN design and demonstrate that carefully constructed input perturbations can yield well-calibrated probabilistic forecasts without additional training cost, supporting the feasibility of ensemble GNNs for operational regional ocean prediction.