# Data Assimilation with Machine Learning Surrogate Models: A Case Study with FourCastNet

arXiv: https://arxiv.org/abs/2405.13180 · HTML: https://mlsanity.com/paper/2405.13180/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 37 references that are in the map.
- First posted on arXiv 21 May 2024.

## Builds on (most cited first, 9 of 9)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024)
- [Towards physically consistent data-driven weather forecasting: Integrating data assimilation with equivariance-preserving deep spatial transformers](https://mlsanity.com/paper/2103.09360/) (2021)

## Built on by (most cited first, 10 of 10)

- [Project and Generate: Divergence-Free Neural Operators for Incompressible Flows](https://mlsanity.com/paper/2603.24500/) (2026)
- [4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models](https://mlsanity.com/paper/2408.02767/) (2024)
- [Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence](https://mlsanity.com/paper/2507.00719/) (2025)
- [SENDAI: A Hierarchical Sparse-measurement, EfficieNt Data AssImilation Framework](https://mlsanity.com/paper/2601.21664/) (2026)
- [Ensemble data assimilation to diagnose AI-based weather prediction model: A case with ClimaX version 0.3.1](https://mlsanity.com/paper/2407.17781/) (2024)
- [Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems](https://mlsanity.com/paper/2412.14318/) (2024)
- [Probability calibration for precipitation nowcasting](https://mlsanity.com/paper/2510.00594/) (2025)
- [Bridging Artificial Intelligence and Data Assimilation: The Data-driven Ensemble Forecasting System ClimaX-LETKF](https://mlsanity.com/paper/2512.14444/) (2025)
- [Operator Learning for Smoothing and Forecasting](https://mlsanity.com/paper/2603.20359/) (2026)
- [Auto-differentiable data assimilation: Co-learning of states, dynamics, and filtering algorithms](https://mlsanity.com/paper/2603.20891/) (2026)

## Abstract (arXiv)

Modern data-driven surrogate models for weather forecasting provide accurate short-term predictions but inaccurate and nonphysical long-term forecasts. This paper investigates online weather prediction using machine learning surrogates supplemented with partial and noisy observations. We empirically demonstrate and theoretically justify that, despite the long-time instability of the surrogates and the sparsity of the observations, filtering estimates can remain accurate in the long-time horizon. As a case study, we integrate FourCastNet, a weather surrogate model, within a variational data assimilation framework using partial, noisy ERA5 data. Our results show that filtering estimates remain accurate over a year-long assimilation window and provide effective initial conditions for forecasting tasks, including extreme event prediction.