# Attention-based Convolutional Autoencoders for 3D-Variational Data Assimilation

arXiv: https://arxiv.org/abs/2101.02121 · HTML: https://mlsanity.com/paper/2101.02121/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 98 references that are in the map.
- First posted on arXiv 6 Jan 2021.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [CBAM: Convolutional Block Attention Module](https://mlsanity.com/paper/1807.06521/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Lossy Image Compression with Compressive Autoencoders](https://mlsanity.com/paper/1703.00395/) (2017)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Residual Non-local Attention Networks for Image Restoration](https://mlsanity.com/paper/1903.10082/) (2019)
- [Efficient Object Localization Using Convolutional Networks](https://mlsanity.com/paper/1411.4280/) (2014)
- [LLNet: A Deep Autoencoder Approach to Natural Low-light Image Enhancement](https://mlsanity.com/paper/1511.03995/) (2015)
- [Residual Dense Network for Image Restoration](https://mlsanity.com/paper/1812.10477/) (2018)
- [Deep Autoencoding Models for Unsupervised Anomaly Segmentation in Brain MR Images](https://mlsanity.com/paper/1804.04488/) (2018)
- [Deep Rewiring: Training very sparse deep networks](https://mlsanity.com/paper/1711.05136/) (2017)
- [Variational Autoencoder for Deep Learning of Images, Labels and Captions](https://mlsanity.com/paper/1609.08976/) (2016)
- [Conditional Probability Models for Deep Image Compression](https://mlsanity.com/paper/1801.04260/) (2018)
- [Density Modeling of Images using a Generalized Normalization Transformation](https://mlsanity.com/paper/1511.06281/) (2015)
- [Practical Full Resolution Learned Lossless Image Compression](https://mlsanity.com/paper/1811.12817/) (2018)

## Built on by (most cited first, 15 of 15)

- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Latent Space Data Assimilation by using Deep Learning](https://mlsanity.com/paper/2104.00430/) (2021)
- [Variational Data Assimilation with a Learned Inverse Observation Operator](https://mlsanity.com/paper/2102.11192/) (2021)
- [FengWu-4DVar: Coupling the Data-driven Weather Forecasting Model with 4D Variational Assimilation](https://mlsanity.com/paper/2312.12455/) (2023)
- [AI Foundation Models for Weather and Climate: Applications, Design, and Implementation](https://mlsanity.com/paper/2309.10808/) (2023)
- [Bridging observation, theory and numerical simulation of the ocean using Machine Learning](https://mlsanity.com/paper/2104.12506/) (2021)
- [TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functions](https://mlsanity.com/paper/2409.00244/) (2024)
- [Ensemble Kalman filter in latent space using a variational autoencoder pair](https://mlsanity.com/paper/2502.12987/) (2025)
- [Joint calibration and mapping of satellite altimetry data using trainable variational models](https://mlsanity.com/paper/2110.03405/) (2021)
- [An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes](https://mlsanity.com/paper/2202.06170/) (2022)
- [Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems](https://mlsanity.com/paper/2502.16232/) (2025)
- [Latent Twins](https://mlsanity.com/paper/2509.20615/) (2025)
- [VAE-Var: Variational-Autoencoder-Enhanced Variational Assimilation](https://mlsanity.com/paper/2405.13711/) (2024)
- [ABCD: Trust enhanced Attention based Convolutional Autoencoder for Risk Assessment](https://mlsanity.com/paper/2404.16183/) (2024)

## Abstract (arXiv)

We propose a new 'Bi-Reduced Space' approach to solving 3D Variational Data Assimilation using Convolutional Autoencoders. We prove that our approach has the same solution as previous methods but has significantly lower computational complexity; in other words, we reduce the computational cost without affecting the data assimilation accuracy. We tested the new method with data from a real-world application: a pollution model of a site in Elephant and Castle, London and found that we could reduce the size of the background covariance matrix representation by O(10^3) and, at the same time, increase our data assimilation accuracy with respect to existing reduced space methods.