mlsanityData to 7 Oct 2026

Learning Dynamical Systems from Partial Observations

arXiv 1902.11136 ↗First posted 26 Feb 2019eess.SY cs.LG cs.SYcited by 36

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Abstract (arXiv)

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled by an unknown time-varying differential equation, and the evolution term is estimated from the data, using a neural network. Any future state can then be computed by placing the associated differential equation in an ODE solver. We first evaluate our approach on shallow water and Euler simulations. We find that our method not only demonstrates high quality long-term forecasts, but also learns to produce hidden states closely resembling the true states of the system, without direct supervision on the latter. Additional experiments conducted on challenging, state of the art ocean simulations further validate our findings, while exhibiting notable improvements over classical baselines.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Feb 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 9; 2022: 6; 2023: 8; 2024: 9; 2025: 1; 2026: 3.

36 papers.

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  1. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 207
  2. 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
  3. 2021LEADS: Learning Dynamical Systems that Generalize Across Environmentscited by 39
  4. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 37
  5. 2021A Framework for Machine Learning of Model Error in Dynamical Systemscited by 37
  6. 2022Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networkscited by 33
  7. 2024Out-of-Domain Generalization in Dynamical Systems Reconstructioncited by 33
  8. 2024DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systemscited by 29
  9. 2021Auto-differentiable Ensemble Kalman Filterscited by 28
  10. 2021Hybrid FEM-NN models: Combining artificial neural networks with the finite element methodcited by 24
  11. 2021Reconstructing Nonlinear Dynamical Systems from Multi-Modal Time Seriescited by 16
  12. 2023Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systemscited by 14
24 more
  1. 2024On latent dynamics learning in nonlinear reduced order modelingcited by 14
  2. 2021Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equationscited by 13
  3. 2024Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Responsecited by 13
  4. 2021NeuralPDE: Modelling Dynamical Systems from Datacited by 9
  5. 2023DynaBench: A benchmark dataset for learning dynamical systems from low-resolution datacited by 8
  6. 2022Continuous-time identification of dynamic state-space models by deep subspace encodingcited by 5
  7. 2023Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Datacited by 5
  8. 2024Advancing Generalization in PINNs through Latent-Space Representationscited by 5
  9. 2022SPADE4: Sparsity and Delay Embedding based Forecasting of Epidemicscited by 4
  10. 2022A memory-efficient neural ODE framework based on high-level adjoint differentiationcited by 3
  11. 2023Learning Absorption Rates in Glucose-Insulin Dynamics from Meal Covariatescited by 3
  12. 2024Learning Macroscopic Dynamics from Partial Microscopic Observationscited by 3
  13. 2021Reconstructing a dynamical system and forecasting time series by self-consistent deep learningcited by 2
  14. 2024DDE-Find: Learning Delay Differential Equations from Noisy, Limited Datacited by 1
  15. 2025Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Datacited by 1
  16. 2022A Deep Learning Approach To Estimation Using Measurements Received Over a Networkcited by 0
  17. 2022Unraveled Multilevel Transformation Networks for Predicting Sparsely-Observed Spatiotemporal Dynamicscited by 0
  18. 2023Stability of implicit neural networks for long-term forecasting in dynamical systemscited by 0
  19. 2023TaylorPDENet: Learning PDEs from non-grid Datacited by 0
  20. 2024GrINd: Grid Interpolation Network for Scattered Observationscited by 0
  21. 2024Rational-WENO: A lightweight, physically-consistent three-point weighted essentially non-oscillatory schemecited by 0
  22. 2026Diagnosing Under-Development of Irreversible Processes in Video Generationcited by 0
  23. 2026Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanismcited by 0
  24. 2026Learning PDE Dynamics between Submanifolds Using Green's Observation Operatorscited by 0