mlsanityData to 14 Oct 2026

Deep learning to discover and predict dynamics on an inertial manifold

arXiv 2001.04263 ↗First posted 20 Dec 2019cs.LG physics.flu-dyncited by 43

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Abstract (arXiv)

A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM), and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension reduction transforms between coordinates in the full state space and on the IM. Additional neural networks predict time-evolution on the IM. The formalism accounts for translation invariance and energy conservation, and substantially outperforms linear dimension reduction, reproducing very well key dynamic and statistical features of the attractor.

Key facts. Cited by 43 papers in the map (data through 14 Oct 2026). First posted on arXiv 20 Dec 2019.

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Citing papers per year: 2021: 5; 2022: 6; 2023: 13; 2024: 7; 2025: 5; 2026: 7.

43 papers.

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  1. 2022Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoderscited by 58
  2. 2021Data-driven discovery of intrinsic dynamicscited by 45
  3. 2023Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flowscited by 31
  4. 2021Data-Driven Reduced-Order Modeling of Spatiotemporal Chaos with Neural Ordinary Differential Equationscited by 30
  5. 2023Generative learning for nonlinear dynamicscited by 22
  6. 2022Data-driven control of spatiotemporal chaos with reduced-order neural ODE-based models and reinforcement learningcited by 17
  7. 2021Learning normal form autoencoders for data-driven discovery of universal,parameter-dependent governing equationscited by 15
  8. 2023Autoencoders for discovering manifold dimension and coordinates in data from complex dynamical systemscited by 13
  9. 2021Nonlinear proper orthogonal decomposition for convection-dominated flowscited by 11
  10. 2023Interpretable learning of effective dynamics for multiscale systemscited by 11
  11. 2023Slow Invariant Manifolds of Singularly Perturbed Systems via Physics-Informed Machine Learningcited by 10
  12. 2022Data-driven low-dimensional dynamic model of Kolmogorov flowcited by 9
31 more
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  4. 2023Nonlinear dimensionality reduction then and now: AIMs for dissipative PDEs in the ML eracited by 7
  5. 2024Stability analysis of chaotic systems in latent spacescited by 7
  6. 2024Generative Learning for Forecasting the Dynamics of Complex Systemscited by 6
  7. 2023Turbulence control in plane Couette flow using low-dimensional neural ODE-based models and deep reinforcement learningcited by 5
  8. 2023Recurrences reveal shared causal drivers of complex time seriescited by 5
  9. 2023Enhancing Predictive Capabilities in Data-Driven Dynamical Modeling with Automatic Differentiation: Koopman and Neural ODE Approachescited by 5
  10. 2022Learning effective dynamics from data-driven stochastic systemscited by 3
  11. 2023Learning to Decouple Complex Systemscited by 3
  12. 2025Deep Learning of the Evolution Operator Enables Forecasting of Out-of-Training Dynamics in Chaotic Systemscited by 3
  13. 2025Learning solution operator of dynamical systems with diffusion maps kernel ridge regressioncited by 3
  14. 2022Decentralized digital twins of complex dynamical systemscited by 2
  15. 2023Building symmetries into data-driven manifold dynamics models for complex flows: application to two-dimensional Kolmogorov flowcited by 2
  16. 2024RefreshNet: Learning Multiscale Dynamics through Hierarchical Refreshingcited by 2
  17. 2024On instabilities in neural network-based physics simulatorscited by 2
  18. 2026Geometric regularization of autoencoders via observed stochastic dynamicscited by 2
  19. 2026Information bottleneck for learning the phase space of dynamics from high-dimensional experimental datacited by 1
  20. 2022Prospects of federated machine learning in fluid dynamicscited by 0
  21. 2024A Novel Paradigm in Solving Multiscale Problemscited by 0
  22. 2024Data-driven low-dimensional model of a sedimenting flexible fibercited by 0
  23. 2024Inferring stability properties of chaotic systems on autoencoders' latent spacescited by 0
  24. 2025Invariant Manifolds of Discrete-time Dynamical Systems with Nonlinear Exosystems via Hybrid Physics-Informed Neural Networkscited by 0
  25. 2025Blending data and physics for reduced-order modeling of systems with spatiotemporal chaotic dynamicscited by 0
  26. 2025Conditioning on PDE Parameters to Generalise Deep Learning Emulation of Stochastic and Chaotic Dynamicscited by 0
  27. 2026From Data to Laws: Neural Discovery of Conservation Laws Without False Positivescited by 0
  28. 2026Inertial Manifold Neural Operator for Dissipative Time-Dependent Partial Differential Equationscited by 0
  29. 2026Rollout-Decoded Reconstruction for Long-Horizon Prediction in Latent World Modelscited by 0
  30. 2026Beyond Compression: Training Latent Representations for Stable Long-Horizon Rollout in Neural Surrogate Solverscited by 0
  31. 2026Latent-Lagrangian Neural Networks for Reduced Order Modeling of Non-autonomous Nonlinear Dynamical Systemscited by 0