This repo contains my work on variational autoencoders applied to generative design. For a thorough documentation on the mathematical principles of the work, it would be adequate to read : https://arxiv.org/abs/2205.02102

The objective of this project has been to live-compute some measure of an Airfoil's performance with respect to to it's design. In this case, the perfomance indicator selected was the lift polar.

The study case for the application of this technique has been the design extrapolation of 11 NACA Airfoils. This data has been extracted from: http://airfoiltools.com/airfoil/naca4digit. Imported as .txt files in the Airfoils folder. The same operation was performed by the polars of each of these Airfoils, folder Polars.

The functioning of this example is as follows: The design of each Airfoil and its lift polar (C_l vs α, being α each Airfoil's angle of attack) are mapped to two 2-Dimensional latent spaces (One for the Airfoil and one for it's polar function). We will be able to move through the latent space in real time with two ranges embedded in an HTML file.

For this purpose, 3 Neural networks are constructed in the code. Two Variational autoencoders (One for the Airfoil designs and another for their polars) and one feed forward neural network that maps the latent spaces between the two. The figure below shows the probabilistic distributions of each Airfoil in the latent space. This is, each of the 11 normal distributions below corresponds to one of the Airfoils the networks were trained with. This 2D space is mapped into the corresponding polar 2D space via the mapper (the distributions of the Airfoil polars will not be located on the same points).

Essentially, the VAEs allow us to simplify a 2n dimensional space (Being n the number of points of each airfoil in 2D space) into a 2D space, being the design optimization much more manageable. VAEs are able to "generate" the corresponding design from a point in the latent space, hence the name Generative Design. The results obtained after training are shown below:

There are 2 main advantages that I see in the application of this technique:

• In many optimization problems, it is very difficult to state on clear terms the domain scope of the design. This is, in the case of an Airfoil design optimization, what constitutes an Airfoil? What are the series of restrictions that one must pose to ensure that the optimization result provides an Airfoil? The answer to this question is very complex and in many cases left unanswered, carrying out the optimization many times by hand. The VAE not only reduces the dimensionality of the search domain, but also (when correctly tuned) restricts the scope of the search to "shapes" that can be characterized as Airfoils.

• The extrapolation of this design to 3D objects is immediate (Increasing the network complexity). (This is what was performed in https://arxiv.org/abs/2205.02102)

The fact that a VAE is able to contraint the search space to a "valid answers" subspace can be also used for some XAI problems such as Counterfactual generation (https://christophm.github.io/interpretable-ml-book/counterfactual.html): http://rvc.eng.miami.edu/Paper/2018/IJMDEM2018-2.pdf

Main References:

Main concepts of VAEs clearly explained: https://www.youtube.com/watch?v=9zKuYvjFFS8&t=604s&ab_channel=ArxivInsights

For information about the VAE implementations: https://keras.io/examples/generative/vae/

For information about Polars, Airfoils and basic aerodynamic concepts: https://en.wikipedia.org/wiki/Drag_curve, http://airfoiltools.com/polar/index

Contact: [email protected]