Scalable Parameterization of Aerodynamic Shapes Using Deep-Learning-Based Geometric Compression

The design of aerodynamic parts requires a mathematical representation of the geometric shape, through which systematic modifications can be made in an iterative design procedure. While numerous parameterization formulations are available for airfoil design in the two-dimensional setting, for the three-dimensional case, a constructive parameterization tool that is applicable across a wide range of problem settings is yet to be put forward. In this paper, a scalable parameterization of aerodynamic designs is created by applying deep learning for compression of individual geometries and leveraging meta-learning to fit the corresponding distributions. Compression is achieved by reformulating the shape’s descriptor from discrete grids to continuous neural representations of the implicit geometric field data; the corresponding variable number can be reduced by an order of magnitude or more, reducing the associated design space and parameterization complexity. In this work, the approach has been applied to both two- and three-dimensional problem settings through airfoil and wing parameterizations and benchmarked against alternative deep learning parameterization approaches as well as the discrete field alternative. Results show that the method is competitive—and in many cases outperforms—the benchmarks, while achieving strong scalability with regard to both geometric field resolution and spatial dimensionality.