mlsanityData to 14 Oct 2026

Data Assimilation: A Mathematical Introduction

arXiv 1506.07825 ↗First posted 25 Jun 2015math.DS math.OC stat.MEcited by 27

Not on the map. Why?

Abstract (arXiv)

These notes provide a systematic mathematical treatment of the subject of data assimilation.

Key facts. Cited by 27 papers in the map (data through 14 Oct 2026). First posted on arXiv 25 Jun 2015.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 6; 2022: 3; 2023: 2; 2024: 5; 2025: 4; 2026: 7.

27 papers.

Sort:

By area:

  1. 2021Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Componentscited by 18
  2. 2022Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effectscited by 15
  3. 2023Leveraging arbitrary mobile sensor trajectories with shallow recurrent decoder networks for full-state reconstructioncited by 12
  4. 2025Learning Enhanced Ensemble Filterscited by 11
  5. 2021Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networkscited by 10
  6. 2024Learning Optimal Filters Using Variational Inferencecited by 9
  7. 2024Nonlinear Assimilation via Score-based Sequential Langevin Samplingcited by 8
  8. 2023CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boostingcited by 7
  9. 2021Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto-Sivashinsky test casecited by 6
  10. 2022Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilationcited by 5
  11. 2021Low-rank statistical finite elements for scalable model-data synthesiscited by 3
  12. 2025Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systemscited by 3
15 more
  1. 2021Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilationcited by 2
  2. 2024Ensemble Transport Filter via Optimized Maximum Mean Discrepancycited by 2
  3. 2026ProFlow: Zero-Shot Physics-Consistent Sampling via Proximal Flow Guidancecited by 2
  4. 2026LatentFlow: A General Framework for Conditioning Stochastic Processescited by 2
  5. 2025Bridging Prediction and Attribution: Identifying Forward and Backward Causal Influence Ranges Using Assimilative Causal Inferencecited by 1
  6. 2025Reinforcement learning based data assimilation for unknown state modelcited by 1
  7. 2021ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systemscited by 0
  8. 2022Unsupervised learning of observation functions in state-space models by nonparametric moment methodscited by 0
  9. 2024Preserving linear invariants in ensemble filtering methodscited by 0
  10. 2024Machine Learning for Complex Systems with Abnormal Pattern by Exception Maximization Outlier Detection Methodcited by 0
  11. 2026Hierarchical Inference and Closure Learning via Adaptive Surrogates for ODEs and PDEscited by 0
  12. 2026A Continuous-Time Ensemble Kalman-Bucy Smoother for Causal Inference and Model Discoverycited by 0
  13. 2026Dynestyx: A Probabilistic Programming Library for Dynamical Systemscited by 0
  14. 2026FREESIA: Covariance-Aware Posterior Transport for Expressive and Scalable Data Assimilationcited by 0
  15. 2026LD-EnFF: Latent-Dynamics Ensemble Flow Filtering for Data Assimilation with Sparse Observationscited by 0