Data-Driven Methods in Fluid Dynamics: Sparse Classification from Experimental Data

  • Zhe Bai
  • Steven L. Brunton
  • Bingni W. Brunton
  • J. Nathan Kutz
  • Eurika Kaiser
  • Andreas Spohn
  • Bernd R. Noack


This work explores the use of data-driven methods, including machine learning and sparse sampling, for systems in fluid dynamics. In particular, camera images of a transitional separation bubble are used with dimensionality reduction and supervised classification techniques to discriminate between an actuated and an unactuated flow. After classification is demonstrated on full-resolution image data, similar classification performance is obtained using heavily subsampled pixels from the images. Finally, a sparse sensor optimization based on compressed sensing is used to determine optimal pixel locations for accurate classification. With 5–10 specially selected sensors, the median cross-validated classification accuracy is ≥ 97 %, as opposed to a random set of 5–10 pixels, which results in classification accuracy of 70–80 %. The methods developed here apply broadly to high-dimensional data from fluid dynamics experiments. Relevant connections between sparse sampling and the representation of high-dimensional data in a low-rank feature space are discussed.


Flow visualization Reduced-order models Proper orthogonal decomposition Machine learning Classification Sparse sampling Compressed sensing 



We would like to thank Mark Glauser for valuable suggestions that have improved this work, especially encouraging us to elaborate on the connection to big data. We gratefully acknowledge discussions with Josh Proctor about sparsity methods in machine learning. SLB and ZB acknowledge generous support from the Department of Energy (DOE DE-EE0006785). SLB also acknowledges support from the Air Force Office of Scientific Research (FA9550-14-1-0398) and from the University of Washington Department of Mechanical Engineering. SLB and BWB acknowledge sponsorship by the UW eScience Institute as Data Science Fellows. EK, AS, and BRN acknowledge additional support by the ANR SepaCoDe (ANR-11-BS09-018) and ANR TUCOROM (ANR-10-CEXC-0015).


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Zhe Bai
    • 1
  • Steven L. Brunton
    • 1
  • Bingni W. Brunton
    • 2
  • J. Nathan Kutz
    • 3
  • Eurika Kaiser
    • 4
  • Andreas Spohn
    • 5
  • Bernd R. Noack
    • 6
    • 7
  1. 1.Department of Mechanical EngineeringUniversity of WashingtonSeattleUSA
  2. 2.Department of BiologyUniversity of WashingtonSeattleUSA
  3. 3.Department of Applied MathematicsUniversity of WashingtonSeattleUSA
  4. 4.Départment Fluides, Thermique, CombustionInstitut PPRIME, CNRS – Université de Poitiers – ENSMAPoiters CEDEXFrance
  5. 5.Institute PPRIMECNRS – Université de Poitiers – ENSMAPoitiers CEDEXFrance
  6. 6.LIMSI-CNRS, Rue John von NeumannCampus Universitaire d’OrsayOrsayFrance
  7. 7.Institut für StrömungsmechanikTechnische Universit’́at BraunschweigBraunschweigGermany

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