mlsanityData to 7 Oct 2026

Latent Space Data Assimilation by using Deep Learning

arXiv 2104.00430 ↗First posted 1 Apr 2021cs.LG cs.NA math.NAcited by 29

Not on the map. Why?

Abstract (arXiv)

Performing Data Assimilation (DA) at a low cost is of prime concern in Earth system modeling, particularly at the time of big data where huge quantities of observations are available. Capitalizing on the ability of Neural Networks techniques for approximating the solution of PDE's, we incorporate Deep Learning (DL) methods into a DA framework. More precisely, we exploit the latent structure provided by autoencoders (AEs) to design an Ensemble Transform Kalman Filter with model error (ETKF-Q) in the latent space. Model dynamics are also propagated within the latent space via a surrogate neural network. This novel ETKF-Q-Latent (thereafter referred to as ETKF-Q-L) algorithm is tested on a tailored instructional version of Lorenz 96 equations, named the augmented Lorenz 96 system: it possesses a latent structure that accurately represents the observed dynamics. Numerical experiments based on this particular system evidence that the ETKF-Q-L approach both reduces the computational cost and provides better accuracy than state of the art algorithms, such as the ETKF-Q.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). Builds on 25 of its 71 references that are in the map. First posted on arXiv 1 Apr 2021.

Builds on

25 of 71 references.

References · 25

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,267
  3. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  4. 2013Intriguing properties of neural networkscited by 5,114
  5. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,976
  6. 2014Sequence to Sequence Learning with Neural Networkscited by 2,974
  7. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  8. 2016Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translationcited by 1,471
  9. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  10. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
  11. 2018AllenNLP: A Deep Semantic Natural Language Processing Platformcited by 347
  12. 2017Stable Architectures for Deep Neural Networkscited by 340
13 more
  1. 2020ReZero is All You Need: Fast Convergence at Large Depthcited by 260
  2. 2019Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systemscited by 203
  3. 2017Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equationscited by 158
  4. 2018Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networkscited by 155
  5. 2018Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flowcited by 97
  6. 2018Deep Learning of Vortex Induced Vibrationscited by 74
  7. 2020Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 modelcited by 72
  8. 2019Differentiable Physics-informed Graph Networkscited by 25
  9. 2019IMEXnet: A Forward Stable Deep Neural Networkcited by 22
  10. 2018Towards a Robust Parameterization for Conditioning Facies Models Using Deep Variational Autoencoders and Ensemble Smoothercited by 16
  11. 2021Attention-based Convolutional Autoencoders for 3D-Variational Data Assimilationcited by 15
  12. 2020Latent Space Subdivision: Stable and Controllable Time Predictions for Fluid Flowcited by 13
  13. 2020Detection of Iterative Adversarial Attacks via Counter Attackcited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 1; 2023: 6; 2024: 9; 2025: 4; 2026: 8.

29 papers.

Sort:

By area:

  1. 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
  2. 2024Deep Generative Data Assimilation in Multimodal Settingcited by 28
  3. 2022Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Modelscited by 24
  4. 2023FengWu-4DVar: Coupling the Data-driven Weather Forecasting Model with 4D Variational Assimilationcited by 22
  5. 2021Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimationcited by 20
  6. 2023Towards an end-to-end artificial intelligence driven global weather forecasting systemcited by 20
  7. 2023Efficient deep data assimilation with sparse observations and time-varying sensorscited by 14
  8. 2024LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observationscited by 10
  9. 2023Latent assimilation with implicit neural representations for unknown dynamicscited by 8
  10. 2024FNP: Fourier Neural Processes for Arbitrary-Resolution Data Assimilationcited by 8
  11. 2024State-observation augmented diffusion model for nonlinear assimilation with unknown dynamicscited by 7
  12. 2024Accurate deep learning-based filtering for chaotic dynamics by identifying instabilities without an ensemblecited by 7
17 more
  1. 2024TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functionscited by 5
  2. 2025Ensemble Kalman filter in latent space using a variational autoencoder paircited by 5
  3. 2025Align-DA: Align Score-based Atmospheric Data Assimilation with Multiple Preferencescited by 5
  4. 2024Generating Unseen Nonlinear Evolution in Sea Surface Temperature Using a Deep Learning-Based Latent Space Data Assimilation Frameworkcited by 3
  5. 2025Tensor-Var: Efficient Four-Dimensional Variational Data Assimilationcited by 3
  6. 2025Bridging Idealized and Operational Models: An Explainable AI Framework for Earth System Emulatorscited by 3
  7. 2026Latent Autoencoder Ensemble Kalman Filter for Nonlinear Data assimilationcited by 3
  8. 2024Review on Fault Diagnosis and Fault-Tolerant Control Scheme for Robotic Manipulators: Recent Advances in AI, Machine Learning, and Digital Twincited by 2
  9. 2026Neural ensemble Kalman filter: Data assimilation for compressible flows with shockscited by 2
  10. 2024The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantificationcited by 1
  11. 2026Accurate and Efficient Hybrid-Ensemble Atmospheric Data Assimilation in Latent Space with Uncertainty Quantificationcited by 1
  12. 2026ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiabilitycited by 1
  13. 2023Generating observation guided ensembles for data assimilation with denoising diffusion probabilistic modelcited by 0
  14. 2026Ensemble Controlled-Flow Filtering for Implicit Data Assimilationcited by 0
  15. 2026Incomplete Observations Boost Evolutionary Performance in Ocean Modelingcited by 0
  16. 2026PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilationcited by 0
  17. 2026Variational Augmented Invertible Koopman Autoencoder for probabilistic time series forecastingcited by 0