# Development of an offline and online hybrid model for the Integrated Forecasting System

arXiv: https://arxiv.org/abs/2403.03702 · HTML: https://mlsanity.com/paper/2403.03702/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 44 references that are in the map.
- First posted on arXiv 6 Mar 2024.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [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)
- [Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Model](https://mlsanity.com/paper/1909.04711/) (2019)
- [Using machine learning to correct model error in data assimilation and forecast applications](https://mlsanity.com/paper/2010.12605/) (2020)
- [Combining data assimilation and machine learning to infer unresolved scale parametrisation](https://mlsanity.com/paper/2009.04318/) (2020)
- [Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization](https://mlsanity.com/paper/2001.06270/) (2020)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [A posteriori learning for quasi-geostrophic turbulence parametrization](https://mlsanity.com/paper/2204.03911/) (2022)
- [Supervised learning from noisy observations: Combining machine-learning techniques with data assimilation](https://mlsanity.com/paper/2007.07383/) (2020)
- [Combining Machine Learning with Knowledge-Based Modeling for Scalable Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal Systems](https://mlsanity.com/paper/2002.05514/) (2020)
- [Applying machine learning to improve simulations of a chaotic dynamical system using empirical error correction](https://mlsanity.com/paper/1904.10904/) (2019)
- [Online learning of both state and dynamics using ensemble Kalman filters](https://mlsanity.com/paper/2006.03859/) (2020)
- [Online model error correction with neural networks in the incremental 4D-Var framework](https://mlsanity.com/paper/2210.13817/) (2022)
- [A comparison of combined data assimilation and machine learning methods for offline and online model error correction](https://mlsanity.com/paper/2107.11114/) (2021)
- [Super-resolution data assimilation](https://mlsanity.com/paper/2109.08017/) (2021)
- [State, global and local parameter estimation using local ensemble Kalman filters: applications to online machine learning of chaotic dynamics](https://mlsanity.com/paper/2107.11253/) (2021)

## Built on by (most cited first, 2 of 2)

- [Balancing Accuracy and Speed: A Multi-Fidelity Ensemble Kalman Filter with a Machine Learning Surrogate Model](https://mlsanity.com/paper/2512.12276/) (2025)
- [Accounting for model error in ensemble variational data assimilation through learned generative dynamics](https://mlsanity.com/paper/2610.17333/) (2026)

## Abstract (arXiv)

In recent years, there has been significant progress in the development of fully data-driven global numerical weather prediction models. These machine learning weather prediction models have their strength, notably accuracy and low computational requirements, but also their weakness: they struggle to represent fundamental dynamical balances, and they are far from being suitable for data assimilation experiments. Hybrid modelling emerges as a promising approach to address these limitations. Hybrid models integrate a physics-based core component with a statistical component, typically a neural network, to enhance prediction capabilities. In this article, we propose to develop a model error correction for the operational Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts using a neural network. The neural network is initially pre-trained offline using a large dataset of operational analyses and analysis increments. Subsequently, the trained network is integrated into the IFS within the Object-Oriented Prediction System (OOPS) so as to be used in data assimilation and forecast experiments. It is then further trained online using a recently developed variant of weak-constraint 4D-Var. The results show that the pre-trained neural network already provides a reliable model error correction, which translates into reduced forecast errors in many conditions and that the online training further improves the accuracy of the hybrid model in many conditions.