Regularizing invertible neural networks for airfoil design through dimension reduction

Glaws, Andrew; Hokanson, Jeffrey M.; King, Ruth; Vijayakumar, Ganesh

doi:10.2514/6.2022-1098

Cited by 2 publications

(2 citation statements)

References 21 publications

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“…The CST method (and other explicit basis representations) often couples linear scaling of the shape (affine deformations) and undulating perturbations. Affine deformations-like changes in thickness, camber, and orientation-are often constrained in design problems (e.g., changes in thickness, Reynolds number, or angle-of-attack) and result in relatively well-understood physical impacts on aerodynamic performance; while undulating perturbations are of increasing interest to airfoil design (Berguin et al, 2015;Glaws, Hokanson, et al, 2022;Grey & Constantine, 2018). G2Aero decouples linear scaling and undulations by defining undulations as the set of all deformations modulo linear scaling of discrete curves.…”

Section: Comparison With Existing Methodsmentioning

confidence: 99%

“…Recent rapid development of artificial intelligence (AI) and machine learning (ML) algorithms made an airfoil design a growing area of research once again. Shape representations that better regularize deformations and reduce the dimension of the design space can have a significant impact in AI and ML applications (Chen et al, 2020;Glaws, Hokanson, et al, 2022;Grey & Constantine, 2018).…”

Section: Statement Of Needmentioning

confidence: 99%

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G2Aero: A Python package for separable shape tensors

Doronina,

Grey,

Glaws

2023

JOSS

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G2Aero is a Python package for the design and deformation of discrete planar curves and tubular surfaces using a geometric data-driven approach. G2Aero utilizes a topology of product manifolds: the Grassmannian, 𝒢(𝑛, 2)-the set of 2-dimensional subspaces in ℝ 𝑛 -and the symmetric positive-definite (SPD) manifold, 𝑆 2 ++ -the set of 2×2 SPD matrices. The package provides a novel framework for representing separable deformations to shapes, which consist of stretching, scaling, rotating, and translating-also known as affine deformations-and a set of complementary deformations-which we refer to as undulation-type deformations.

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Section: Comparison With Existing Methodsmentioning

confidence: 99%

Section: Statement Of Needmentioning

confidence: 99%

G2Aero: A Python package for separable shape tensors

Doronina,

Grey,

Glaws

2023

JOSS

Self Cite

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Separable shape tensors for aerodynamic design

Grey

Доронина

Glaws

2023

Journal of Computational Design and Engineering

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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.

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Regularizing invertible neural networks for airfoil design through dimension reduction

Cited by 2 publications

References 21 publications

G2Aero: A Python package for separable shape tensors

G2Aero: A Python package for separable shape tensors

Separable shape tensors for aerodynamic design

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