Grassmannian Shape Representations for Aerodynamic Applications

Research output: NRELPoster


Airfoil shape design is a classical problem in engineering, science, and manufacturing. Our motivation is to combine principled physics-based considerations for the shape design problem with modern computational techniques informed by a data-driven approach. Traditional analyses of airfoil shapes emphasize a flow-based sensitivity to deformations which can be represented generally by affine transformations (rotation, scaling, shearing, shifting). We present a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) improved low-dimensional parameter domain for inferential statistics, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes.
Original languageAmerican English
StatePublished - 2022

Publication series

NamePresented at the Association for the Advancement of Artificial Intelligence (AAAI-22), 22 February - 1 March 2022

NREL Publication Number

  • NREL/PO-2C00-82154


  • blade representation
  • data-driven deformations
  • Grassmannian
  • principal geodesic analysis
  • shape representation


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