mlsanityData to 7 Oct 2026

Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations

arXiv 2108.03561 ↗First posted 8 Aug 2021cs.LG physics.comp-ph physics.data-ancited by 20

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Abstract (arXiv)

We present a supervised learning method to learn the propagator map of a dynamical system from partial and noisy observations. In our computationally cheap and easy-to-implement framework a neural network consisting of random feature maps is trained sequentially by incoming observations within a data assimilation procedure. By employing Takens' embedding theorem, the network is trained on delay coordinates. We show that the combination of random feature maps and data assimilation, called RAFDA, outperforms standard random feature maps for which the dynamics is learned using batch data.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 25 of its 67 references that are in the map. First posted on arXiv 8 Aug 2021.

Builds on

25 of 67 references.

References · 25

  1. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  2. 2014Breaking the Curse of Dimensionality with Convex Neural Networkscited by 329
  3. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  4. 2021Next Generation Reservoir Computingcited by 160
  5. 2018Deep learning to represent sub-grid processes in climate modelscited by 156
  6. 2015On the Equivalence between Kernel Quadrature Rules and Random Feature Expansionscited by 136
  7. 2020Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don'tcited by 94
  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. 2018Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Modelcited by 57
  10. 2017Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulationscited by 51
  11. 2019Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Modelcited by 45
  12. 2020Combining data assimilation and machine learning to infer unresolved scale parametrisationcited by 40
13 more
  1. 2020Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximizationcited by 37
  2. 2021A Framework for Machine Learning of Model Error in Dynamical Systemscited by 37
  3. 2019Machine Learning for Prediction with Missing Dynamicscited by 27
  4. 2020Supervised learning from noisy observations: Combining machine-learning techniques with data assimilationcited by 27
  5. 2020Combining Machine Learning with Knowledge-Based Modeling for Scalable Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal Systemscited by 23
  6. 2021Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Componentscited by 18
  7. 2020Online learning of both state and dynamics using ensemble Kalman filterscited by 15
  8. 2017Machine Learning, Deepest Learning: Statistical Data Assimilation Problemscited by 13
  9. 2021Reservoir Computing as a Tool for Climate Predictability Studiescited by 13
  10. 2020Kernel-based Prediction of Non-Markovian Time Seriescited by 9
  11. 2019Leveraging Bayesian Analysis To Improve Accuracy of Approximate Modelscited by 2
  12. 2021Forecasting Using Reservoir Computing: The Role of Generalized Synchronizationcited by 2
  13. 2020Combining Ensemble Kalman Filter and Reservoir Computing to predict spatio-temporal chaotic systems from imperfect observations and modelscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 2; 2023: 2; 2024: 9; 2025: 3; 2026: 3.

20 papers.

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  1. 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
  2. 2022Catch-22s of reservoir computingcited by 11
  3. 2024LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observationscited by 10
  4. 2022Deep learning delay coordinate dynamics for chaotic attractors from partial observable datacited by 8
  5. 2024CGKN: A Deep Learning Framework for Modeling Complex Dynamical Systems and Efficient Data Assimilationcited by 7
  6. 2025Learning dynamical systems with hit-and-run random feature mapscited by 7
  7. 2021Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto-Sivashinsky test casecited by 6
  8. 2024CGNSDE: Conditional Gaussian Neural Stochastic Differential Equation for Modeling Complex Systems and Data Assimilationcited by 6
  9. 2024How more data can hurt: Instability and regularization in next-generation reservoir computingcited by 5
  10. 2024Stable generative modeling using Schr"odinger bridgescited by 3
  11. 2025iPINNER: An Iterative Physics-Informed Neural Network with Ensemble Kalman Filtercited by 3
  12. 2024On the choice of the non-trainable internal weights in random feature mapscited by 2
8 more
  1. 2025RL-DAUNCE: Reinforcement Learning-Driven Data Assimilation with Uncertainty-Aware Constrained Ensemblescited by 2
  2. 2024Topological Approach for Data Assimilationcited by 1
  3. 2024Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systemscited by 1
  4. 2026Auto-differentiable data assimilation: Co-learning of states, dynamics, and filtering algorithmscited by 1
  5. 2023Autoregressive with Slack Time Series Model for Forecasting a Partially-Observed Dynamical Time Seriescited by 0
  6. 2024Forecasting the Forced van der Pol Equation with Frequent Phase Shifts Using Reservoir Computingcited by 0
  7. 2026Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regressioncited by 0
  8. 2026Inference of Unknown Dynamical Components Using Next Generation Reservoir Computing: From Chaotic Systems to Climate Datacited by 0