mlsanityData to 7 Oct 2026

Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows

arXiv 2109.01514 ↗First posted 3 Sep 2021physics.flu-dyn cs.LG physics.comp-phcited by 44

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Abstract (arXiv)

We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow-field data useful for flow analysis, reduced-order modeling, and flow control. Our approach is based on β-variational autoencoders (β-VAEs) and convolutional neural networks (CNNs), which allow us to extract non-linear modes from multi-scale turbulent flows while encouraging the learning of independent latent variables and penalizing the size of the latent vector. Moreover, we introduce an algorithm for ordering VAE-based modes with respect to their contribution to the reconstruction. We apply this method for non-linear mode decomposition of the turbulent flow through a simplified urban environment, where the flow-field data is obtained based on well-resolved large-eddy simulations (LESs). We demonstrate that by constraining the shape of the latent space, it is possible to motivate the orthogonality and extract a set of parsimonious modes sufficient for high-quality reconstruction. Our results show the excellent performance of the method in the reconstruction against linear-theory-based decompositions. Moreover, we compare our method with available AE-based models. We show the ability of our approach in the extraction of near-orthogonal modes that may lead to interpretability.

Key facts. Cited by 44 papers in the map (data through 7 Oct 2026). Builds on 15 of its 69 references that are in the map. First posted on arXiv 3 Sep 2021.

Builds on

15 of 69 references.

References · 15

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3 more
  1. 2020Convolutional-network models to predict wall-bounded turbulence from wall quantitiescited by 46
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 7; 2023: 12; 2024: 8; 2025: 8; 2026: 6.

44 papers.

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  1. 2021Enhancing Computational Fluid Dynamics with Machine Learningcited by 137
  2. 2023β-Variational autoencoders and transformers for reduced-order modelling of fluid flowscited by 76
  3. 2023Discovering Causal Relations and Equations from Datacited by 33
  4. 2023A Denoising Diffusion Model for Fluid Field Predictioncited by 31
  5. 2023Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flowscited by 30
  6. 2024Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulationscited by 24
  7. 2022Improving aircraft performance using machine learning: a reviewcited by 19
  8. 2022Data-driven control of spatiotemporal chaos with reduced-order neural ODE-based models and reinforcement learningcited by 16
  9. 2021Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regressioncited by 15
  10. 2022Physics-aware Reduced-order Modeling of Transonic Flow via β-Variational Autoencodercited by 15
  11. 2022Residual-based physics-informed transfer learning: A hybrid method for accelerating long-term CFD simulations via deep learningcited by 14
  12. 2022Predicting the temporal dynamics of turbulent channels through deep learningcited by 10
32 more
  1. 2021A Review of Physics-based Machine Learning in Civil Engineeringcited by 9
  2. 2022A Thermodynamics-informed Active Learning Approach to Perception and Reasoning about Fluidscited by 9
  3. 2025Diff-SPORT: Diffusion-based Sensor Placement Optimization and Reconstruction of Turbulent flows in urban environmentscited by 8
  4. 2022Emerging trends in machine learning for computational fluid dynamicscited by 7
  5. 2023Generative Adversarial Reduced Order Modellingcited by 7
  6. 2023Diffusion model based data generation for partial differential equationscited by 5
  7. 2024Towards aerodynamic surrogate modeling based on β-variational autoencoderscited by 5
  8. 2025Data-Efficient Deep Operator Network for Unsteady Flow: A Multi-Fidelity Approach with Physics-Guided Subsamplingcited by 5
  9. 2024Reduced-order modeling of unsteady fluid flow using neural network ensemblescited by 4
  10. 2024Enhancing Graph U-Nets for Mesh-Agnostic Spatio-Temporal Flow Predictioncited by 4
  11. 2024Machine Learning Applications to Computational Plasma Physics and Reduced-Order Plasma Modeling: A Perspectivecited by 4
  12. 2023Data-driven Nonlinear Parametric Model Order Reduction Framework using Deep Hierarchical Variational Autoencodercited by 3
  13. 2024Thermodynamics-informed super-resolution of scarce temporal dynamics datacited by 3
  14. 2024Decoder Decomposition for the Analysis of the Latent Space of Nonlinear Autoencoders With Wind-Tunnel Experimental Datacited by 3
  15. 2025EquiNO: A Physics-Informed Neural Operator for Multiscale Simulationscited by 3
  16. 2023Predicting the wall-shear stress and wall pressure through convolutional neural networkscited by 2
  17. 2023Physics-Assisted Reduced-Order Modeling for Identifying Dominant Features of Transonic Buffetcited by 2
  18. 2025Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoderscited by 2
  19. 2025Graph-Convolutional-Beta-VAE for Synthetic Abdominal Aorta Aneurysm Generationcited by 2
  20. 2025Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulencecited by 2
  21. 2026Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectivescited by 2
  22. 2026AeroJEPA: Learning Semantic Latent Representations for Scalable 3D Aerodynamic Field Modelingcited by 2
  23. 2024Generalization capabilities and robustness of hybrid models grounded in physics compared to purely deep learning modelscited by 1
  24. 2025Variational Rank Reduction Autoencoders for Generative Thermal Designcited by 1
  25. 2023SpecXAI -- Spectral interpretability of Deep Learning Modelscited by 0
  26. 2023Novel deep learning methods for 3D flow field segmentation and classificationcited by 0
  27. 2023Compact and Intuitive Airfoil Parameterization Method through Physics-aware Variational Autoencodercited by 0
  28. 2025A Critical Assessment of Pattern Comparisons Between POD and Autoencoders in Intraventricular Flowscited by 0
  29. 2026GenDA: Generative Data Assimilation on Complex Urban Areas via Classifier-Free Diffusion Guidancecited by 0
  30. 2026Conditional Neural Field based Reduced Order Model for Dynamic Ditching Load Predictioncited by 0
  31. 2026Advances in Scientific Machine Learning for Coupled Fluid Flow and Transportcited by 0
  32. 2026The balance between compactness and forecast accuracy of data-driven latent-space reduced-order models in controlled wake flowscited by 0