# FengWu-4DVar: Coupling the Data-driven Weather Forecasting Model with 4D Variational Assimilation

arXiv: https://arxiv.org/abs/2312.12455 · HTML: https://mlsanity.com/paper/2312.12455/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 16 Dec 2023.

## Builds on (most cited first, 11 of 11)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [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)
- [Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model](https://mlsanity.com/paper/2001.01520/) (2020)
- [Using machine learning to correct model error in data assimilation and forecast applications](https://mlsanity.com/paper/2010.12605/) (2020)
- [Learning Variational Data Assimilation Models and Solvers](https://mlsanity.com/paper/2007.12941/) (2020)
- [Latent Space Data Assimilation by using Deep Learning](https://mlsanity.com/paper/2104.00430/) (2021)
- [Attention-based Convolutional Autoencoders for 3D-Variational Data Assimilation](https://mlsanity.com/paper/2101.02121/) (2021)

## Built on by (most cited first, 23 of 23)

- [Generalizing Weather Forecast to Fine-grained Temporal Scales via Physics-AI Hybrid Modeling](https://mlsanity.com/paper/2405.13796/) (2024)
- [Towards an end-to-end artificial intelligence driven global weather forecasting system](https://mlsanity.com/paper/2312.12462/) (2023)
- [Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation](https://mlsanity.com/paper/2504.18720/) (2025)
- [Data driven weather forecasts trained and initialised directly from observations](https://mlsanity.com/paper/2407.15586/) (2024)
- [Deep Learning and Foundation Models for Weather Prediction: A Survey](https://mlsanity.com/paper/2501.06907/) (2025)
- [WeatherReal: A Benchmark Based on In-Situ Observations for Evaluating Weather Models](https://mlsanity.com/paper/2409.09371/) (2024)
- [4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models](https://mlsanity.com/paper/2408.02767/) (2024)
- [OMG-HD: A High-Resolution AI Weather Model for End-to-End Forecasts from Observations](https://mlsanity.com/paper/2412.18239/) (2024)
- [Improving Global Weather and Ocean Wave Forecast with Large Artificial Intelligence Models](https://mlsanity.com/paper/2401.16669/) (2024)
- [Gridded Transformer Neural Processes for Large Unstructured Spatio-Temporal Data](https://mlsanity.com/paper/2410.06731/) (2024)
- [Automatic Differentiation-based Full Waveform Inversion with Flexible Workflows](https://mlsanity.com/paper/2412.00486/) (2024)
- [Benchmarking AI-based data assimilation to advance data-driven global weather forecasting](https://mlsanity.com/paper/2408.11438/) (2024)
- [VAE-Var: Variational-Autoencoder-Enhanced Variational Assimilation](https://mlsanity.com/paper/2405.13711/) (2024)
- [TianJi:An autonomous AI meteorologist for discovering physical mechanisms in atmospheric science](https://mlsanity.com/paper/2603.27738/) (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)
- [Thompson Sampling in Function Spaces via Neural Operators](https://mlsanity.com/paper/2506.21894/) (2025)
- [Earth-o1: A Grid-free Observation-native Atmospheric World Model](https://mlsanity.com/paper/2605.06337/) (2026)
- [ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability](https://mlsanity.com/paper/2608.23297/) (2026)
- [FlowDA: Accurate, Low-Latency Weather Data Assimilation via Flow Matching](https://mlsanity.com/paper/2602.06800/) (2026)
- [Station2Radar: query conditioned gaussian splatting for precipitation field](https://mlsanity.com/paper/2603.00418/) (2026)
- [Accurate, Efficient, and Explainable Deep Learning Approaches for Environmental Science Problems](https://mlsanity.com/paper/2605.19366/) (2026)
- [RealBench: Benchmarking Data-Driven Numerical Weather Forecasting Under Operational Conditions and Extreme Event Challenges](https://mlsanity.com/paper/2605.24945/) (2026)

## Abstract (arXiv)

Weather forecasting is a crucial yet highly challenging task. With the maturity of Artificial Intelligence (AI), the emergence of data-driven weather forecasting models has opened up a new paradigm for the development of weather forecasting systems. Despite the significant successes that have been achieved (e.g., surpassing advanced traditional physical models for global medium-range forecasting), existing data-driven weather forecasting models still rely on the analysis fields generated by the traditional assimilation and forecasting system, which hampers the significance of data-driven weather forecasting models regarding both computational cost and forecasting accuracy. In this work, we explore the possibility of coupling the data-driven weather forecasting model with data assimilation by integrating the global AI weather forecasting model, FengWu, with one of the most popular assimilation algorithms, Four-Dimensional Variational (4DVar) assimilation, and develop an AI-based cyclic weather forecasting system, FengWu-4DVar. FengWu-4DVar can incorporate observational data into the data-driven weather forecasting model and consider the temporal evolution of atmospheric dynamics to obtain accurate analysis fields for making predictions in a cycling manner without the help of physical models. Owning to the auto-differentiation ability of deep learning models, FengWu-4DVar eliminates the need of developing the cumbersome adjoint model, which is usually required in the traditional implementation of the 4DVar algorithm. Experiments on the simulated observational dataset demonstrate that FengWu-4DVar is capable of generating reasonable analysis fields for making accurate and efficient iterative predictions.