mlsanityData to 7 Oct 2026

Variational Data Assimilation with a Learned Inverse Observation Operator

arXiv 2102.11192 ↗First posted 22 Feb 2021cs.LG physics.ao-phcited by 28

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Abstract (arXiv)

Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a cornerstone of large scale forecasting applications such as numerical weather prediction. As such, it is implemented in current operational systems of weather forecasting agencies across the globe. However, finding a good initial state poses a difficult optimization problem in part due to the non-invertible relationship between physical states and their corresponding observations. We learn a mapping from observational data to physical states and show how it can be used to improve optimizability. We employ this mapping in two ways: to better initialize the non-convex optimization problem, and to reformulate the objective function in better behaved physics space instead of observation space. Our experimental results for the Lorenz96 model and a two-dimensional turbulent fluid flow demonstrate that this procedure significantly improves forecast quality for chaotic systems.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Builds on 15 of its 38 references that are in the map. First posted on arXiv 22 Feb 2021.

Builds on

15 of 38 references.

References · 15

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2017Deep Image Priorcited by 1,097
  3. 2021Machine learning accelerated computational fluid dynamicscited by 461
  4. 2020WeatherBench: A benchmark dataset for data-driven weather forecastingcited by 272
  5. 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 201
  6. 2020MetNet: A Neural Weather Model for Precipitation Forecastingcited by 128
  7. 2020MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Frameworkcited by 78
  8. 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
  9. 2019Neural reparameterization improves structural optimizationcited by 44
  10. 2020Combining data assimilation and machine learning to infer unresolved scale parametrisationcited by 40
  11. 2020Using machine learning to correct model error in data assimilation and forecast applicationscited by 40
  12. 2021Attention-based Convolutional Autoencoders for 3D-Variational Data Assimilationcited by 15
3 more
  1. 2020Learning Composable Energy Surrogates for PDE Order Reductioncited by 13
  2. 2020Machine-Learned Preconditioners for Linear Solvers in Geophysical Fluid Flowscited by 10
  3. 2018Improving the condition number of estimated covariance matricescited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 6; 2023: 4; 2024: 5; 2025: 6; 2026: 3.

28 papers.

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  1. 2021Efficient and Modular Implicit Differentiationcited by 199
  2. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 190
  3. 2022Forecasting Global Weather with Graph Neural Networkscited by 165
  4. 2022Clifford Neural Layers for PDE Modelingcited by 91
  5. 2023Score-based Data Assimilationcited by 91
  6. 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
  7. 2021Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modelingcited by 59
  8. 2022Learning to Solve PDE-constrained Inverse Problems with Graph Networkscited by 37
  9. 2024Fuxi-DA: A Generalized Deep Learning Data Assimilation Framework for Assimilating Satellite Observationscited by 18
  10. 2023Efficient deep data assimilation with sparse observations and time-varying sensorscited by 14
  11. 2022Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertaintycited by 13
  12. 2021Learning to Assimilate in Chaotic Dynamical Systemscited by 10
16 more
  1. 2025Binned Spectral Power Loss for Improved Prediction of Chaotic Systemscited by 10
  2. 2024Accurate deep learning-based filtering for chaotic dynamics by identifying instabilities without an ensemblecited by 7
  3. 2022Recurrent Neural Networks and Universal Approximation of Bayesian Filterscited by 5
  4. 2023Recurrences reveal shared causal drivers of complex time seriescited by 5
  5. 2024Deep Bayesian Filter for Bayes-faithful Data Assimilationcited by 5
  6. 2024TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functionscited by 5
  7. 2025Tensor-Var: Efficient Four-Dimensional Variational Data Assimilationcited by 3
  8. 2026Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systemscited by 3
  9. 2024VAE-Var: Variational-Autoencoder-Enhanced Variational Assimilationcited by 2
  10. 2021Lifting the Convex Conjugate in Lagrangian Relaxations: A Tractable Approach for Continuous Markov Random Fieldscited by 1
  11. 2025Neural Operator-Based Nonlinear Nudging for Chaotic Dynamical Systemscited by 1
  12. 2025Uncertainty-aware data assimilation through variational inferencecited by 1
  13. 2025Advancing Ocean State Estimation with efficient and scalable AIcited by 1
  14. 2026ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiabilitycited by 1
  15. 2025On the Effect of Neural Field Reparameterization for 4DVARcited by 0
  16. 2026PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilationcited by 0