mlsanityData to 14 Oct 2026

Neural Network Complexity of Chaos and Turbulence

arXiv 2211.15382 ↗First posted 24 Nov 2022cs.LG hep-th nlin.CDcited by 3

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Abstract (arXiv)

Chaos and turbulence are complex physical phenomena, yet a precise definition of the complexity measure that quantifies them is still lacking. In this work we consider the relative complexity of chaos and turbulence from the perspective of deep neural networks. We analyze a set of classification problems, where the network has to distinguish images of fluid profiles in the turbulent regime from other classes of images such as fluid profiles in the chaotic regime, various constructions of noise and real world images. We analyze incompressible as well as weakly compressible fluid flows. We quantify the complexity of the computation performed by the network via the intrinsic dimensionality of the internal feature representations, and calculate the effective number of independent features which the network uses in order to distinguish between classes. In addition to providing a numerical estimate of the complexity of the computation, the measure also characterizes the neural network processing at intermediate and final stages. We construct adversarial examples and use them to identify the two point correlation spectra for the chaotic and turbulent vorticity as the feature used by the network for classification.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 14 of its 67 references that are in the map. First posted on arXiv 24 Nov 2022.

Builds on

14 of 67 references.

References · 14

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,498
  3. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  4. 2016"Why Should I Trust You?": Explaining the Predictions of Any Classifiercited by 5,070
  5. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  6. 2017Towards A Rigorous Science of Interpretable Machine Learningcited by 1,416
  7. 2019Fantastic Generalization Measures and Where to Find Themcited by 513
  8. 2019Machine Learning for Fluid Mechanicscited by 385
  9. 2021Generative Modeling of Turbulencecited by 26
  10. 2020A Perspective on Machine Learning Methods in Turbulence Modellingcited by 23
  11. 2020Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot databasecited by 17
  12. 2018From Deep to Physics-Informed Learning of Turbulence: Diagnosticscited by 14
2 more
  1. 2022Semi-supervised Learning of Partial Differential Operators and Dynamical Flowscited by 6
  2. 2020Complexity for deep neural networks and other characteristics of deep feature representationscited by 2

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Cited by year

Citing papers per year: 2023: 3.

3 papers.

  1. 2023Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulationscited by 8
  2. 2023Turbulence Scaling from Deep Learning Diffusion Generative Modelscited by 8
  3. 2023The Universal Statistical Structure and Scaling Laws of Chaos and Turbulencecited by 2