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Deep Dynamical Modeling and Control of Unsteady Fluid Flows

arXiv 1805.07472 ↗First posted 18 May 2018cs.CE cs.AIcited by 67

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Abstract (arXiv)

The design of flow control systems remains a challenge due to the nonlinear nature of the equations that govern fluid flow. However, recent advances in computational fluid dynamics (CFD) have enabled the simulation of complex fluid flows with high accuracy, opening the possibility of using learning-based approaches to facilitate controller design. We present a method for learning the forced and unforced dynamics of airflow over a cylinder directly from CFD data. The proposed approach, grounded in Koopman theory, is shown to produce stable dynamical models that can predict the time evolution of the cylinder system over extended time horizons. Finally, by performing model predictive control with the learned dynamical models, we are able to find a straightforward, interpretable control law for suppressing vortex shedding in the wake of the cylinder.

Key facts. Cited by 67 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 May 2018.

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Citing papers per year: 2021: 12; 2022: 16; 2023: 11; 2024: 10; 2025: 10; 2026: 8.

67 papers.

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  1. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  2. 2023Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictorscited by 110
  3. 2024Operator Learning: Algorithms and Analysiscited by 84
  4. 2021Solving PDE-constrained Control Problems Using Operator Learningcited by 41
  5. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 37
  6. 2022gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identificationcited by 30
  7. 2022Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamicscited by 30
  8. 2023The transformative potential of machine learning for experiments in fluid mechanicscited by 26
  9. 2025Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraintscited by 26
  10. 2024Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operatorscited by 25
  11. 2025Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networkscited by 24
  12. 2023Multifactor Sequential Disentanglement via Structured Koopman Autoencoderscited by 23
38 more
  1. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  2. 2023Learning invariant representations of time-homogeneous stochastic dynamical systemscited by 17
  3. 2023Solving Inverse Physics Problems with Score Matchingcited by 15
  4. 2024Physics-informed active learning with simultaneous weak-form latent space dynamics identificationcited by 13
  5. 2021An Operator Theoretic Approach for Analyzing Sequence Neural Networkscited by 12
  6. 2021Model reduction for the material point method via an implicit neural representation of the deformation mapcited by 11
  7. 2024Koopman-Assisted Reinforcement Learningcited by 11
  8. 2023Consistent Long-Term Forecasting of Ergodic Dynamical Systemscited by 10
  9. 2023Neural Koopman prior for data assimilationcited by 9
  10. 2021Innovations Autoencoder and its Application in One-class Anomalous Sequence Detectioncited by 7
  11. 2021Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equationscited by 6
  12. 2022Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectoriescited by 6
  13. 2021CKNet: A Convolutional Neural Network Based on Koopman Operator for Modeling Latent Dynamics from Pixelscited by 5
  14. 2023Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Datacited by 5
  15. 2024Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equationscited by 5
  16. 2021Stochastic Adversarial Koopman Model for Dynamical Systemscited by 4
  17. 2022Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilationcited by 4
  18. 2022Half-Inverse Gradients for Physical Deep Learningcited by 3
  19. 2022Lyapunov-Guided Representation of Recurrent Neural Network Performancecited by 3
  20. 2022A Model-Constrained Tangent Slope Learning Approach for Dynamical Systemscited by 3
  21. 2024Stabilizing Backpropagation Through Time to Learn Complex Physicscited by 3
  22. 2024Koopman-Based Surrogate Modelling of Turbulent Rayleigh-B'enard Convectioncited by 3
  23. 2025Physics-Guided Learning of Meteorological Dynamics for Weather Downscaling and Forecastingcited by 3
  24. 2025FluidFormer: Transformer with Continuous Convolution for Particle-based Fluid Simulationcited by 3
  25. 2025AutoHood3D: A Multi-Modal Benchmark for Automotive Hood Design and Fluid-Structure Interactioncited by 3
  26. 2021Geometry encoding for numerical simulationscited by 2
  27. 2021Self-Supervised Decomposition, Disentanglement and Prediction of Video Sequences while Interpreting Dynamics: A Koopman Perspectivecited by 2
  28. 2022Data-driven End-to-end Learning of Pole Placement Control for Nonlinear Dynamics via Koopman Invariant Subspacescited by 2
  29. 2022Physics-Informed Koopman Networkcited by 2
  30. 2022Eigenvalue initialisation and regularisation for Koopman autoencoderscited by 2
  31. 2023Course Correcting Koopman Representationscited by 2
  32. 2025LBM-GNN: Graph Neural Network Enhanced Lattice Boltzmann Methodcited by 2
  33. 2025RheOFormer: A generative transformer model for simulation of complex fluids and flowscited by 2
  34. 2021Meta-Learning for Koopman Spectral Analysis with Short Time-seriescited by 1
  35. 2022Learning Similarity Metrics for Volumetric Simulations with Multiscale CNNscited by 1
  36. 2022Control of Two-way Coupled Fluid Systems with Differentiable Solverscited by 1
  37. 2022Wavelet-based Loss for High-frequency Interface Dynamicscited by 1
  38. 2022Exploring Physical Latent Spaces for High-Resolution Flow Restorationcited by 1

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