# Separable Shape Tensors for Aerodynamic Design

arXiv: https://arxiv.org/abs/2208.04743 · HTML: https://mlsanity.com/paper/2208.04743/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2022.

## Built on by (most cited first, 2 of 2)

- [Explainable Binary Classification of Separable Shape Ensembles](https://mlsanity.com/paper/2410.12994/) (2024)
- [A Riemannian View on Active Subspaces](https://mlsanity.com/paper/2607.25163/) (2026)

## Abstract (arXiv)

Airfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape design problem with modern computational techniques using a data-driven approach. Modern and traditional analyses of 2D and 3D aerodynamic shapes reveal a flow-based sensitivity to specific deformations that can be represented generally by affine transformations (rotation, scaling, shearing, translation). We present a novel representation of shapes that decouples affine-style deformations over a submanifold and a product submanifold principally of the Grassmannian. As an analytic generative model, the separable 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) an improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal 2D shapes.