# Learning 4DVAR inversion directly from observations

arXiv: https://arxiv.org/abs/2211.09741 · HTML: https://mlsanity.com/paper/2211.09741/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 21 references that are in the map.
- First posted on arXiv 17 Nov 2022.

## Builds on (most cited first, 8 of 8)

- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [Stochastic seismic waveform inversion using generative adversarial networks as a geological prior](https://mlsanity.com/paper/1806.03720/) (2018)
- [Using machine learning to correct model error in data assimilation and forecast applications](https://mlsanity.com/paper/2010.12605/) (2020)
- [Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization](https://mlsanity.com/paper/2001.06270/) (2020)
- [Machine Learning, Deepest Learning: Statistical Data Assimilation Problems](https://mlsanity.com/paper/1707.01415/) (2017)

## Built on by (most cited first, 3 of 3)

- [Accurate deep learning-based filtering for chaotic dynamics by identifying instabilities without an ensemble](https://mlsanity.com/paper/2408.04739/) (2024)
- [Combined Optimization of Dynamics and Assimilation with End-to-End Learning on Sparse Observations](https://mlsanity.com/paper/2409.07137/) (2024)
- [Neural Operator-Based Nonlinear Nudging for Chaotic Dynamical Systems](https://mlsanity.com/paper/2508.05778/) (2025)

## Abstract (arXiv)

Variational data assimilation and deep learning share many algorithmic aspects in common. While the former focuses on system state estimation, the latter provides great inductive biases to learn complex relationships. We here design a hybrid architecture learning the assimilation task directly from partial and noisy observations, using the mechanistic constraint of the 4DVAR algorithm. Finally, we show in an experiment that the proposed method was able to learn the desired inversion with interesting regularizing properties and that it also has computational interests.