I am pretty new to neural networks and I would appreciate some guidance... maybe books or articles on the following topic:

I am an airfoil designer. At fixed flow conditions, the pressure on the airfoil wall will be different depending on its geometry, e.g. thickness. For different geometries, I have a large data set of pressure distributions along the airfoil (they can be treated as images). My idea is to use those "pictures" as training data of a neural network (input), in which the output will be the geometry of airfoil. Then, I would like to target a pressure on the wall (picture) and get a nice airfoil design...

Please let me know if you are aware of similar studies and if there is any book to start with!

  • 1
    $\begingroup$ how are the different geometries represented? also as images? $\endgroup$
    – oW_
    Apr 12, 2019 at 23:18
  • $\begingroup$ The inputs, i.e. pressure distribution, can be an image (google.com/…) or an array with numbers. The output, i.e. airfoil shape, can be also an image or a set of equations because I have a method to parametrise it $\endgroup$
    – daxterss
    Apr 14, 2019 at 9:57
  • $\begingroup$ @daxterss, the comment from _oW was looking for clarification to help improve your question. It is generally best to edit any clarifying information into the question. Thanks. $\endgroup$
    – Stephen Rauch
    Apr 14, 2019 at 19:38

2 Answers 2


If I understood correctly you have images similar to a heat-map like Fig 6:

enter image description here

Well, non-natural images related applications can benefit from DNN as much as natural images, but you are unlikely to be able to use any transfer learning technique.

If you have this heat-map-like images (please consider posting some samples) you can try a simple CNN structure. Since you are a starter you could benefit from using this modeler called Ennui and outputting the source-code in Python or Julia, just remember to take a quick class on CNN to understand your options. For a complete course see Stanford's YouTube playlist on CNNs.

Some papers related to it:

You can inspire your models architecture by theirs

If you want a book to cover NN for deep learning try Goodfellow's.

  • $\begingroup$ Thanks a lot for the references Pedro. The idea is that I have a large set of pressure distribution, such as the blue lines in: google.com/… And each figure has associated a shape of the profile. I would like to target a pressure distribution and, using NN (maye other method is better?), get a new airfoil shape $\endgroup$
    – daxterss
    Apr 14, 2019 at 9:51
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    $\begingroup$ Then you should write those curves as a set of points and feed in a fully connected NN, using them as images may not be the best approach $\endgroup$ Apr 14, 2019 at 13:38

You need to consider how to best to represent the geometry of the airfoil (your output) and the pressure distribution (your input). Typically, for airfoils, as you are probably aware, you can do this by parameterizing the shape and pressure by turning them into length N 1D vectors that start and end at the trailing edge.

Bear in mind that as well as the pressure distribution the eventual shape of the airfoil will depend optionally upon M additional variables: the Reynolds number, the angle of incidence, the Mach number (assuming you are dealing with compressible flows) and possibly more. These may need to be included as part of the input vector.

You should then create a network with N+M input neurons, a number of fully connected hidden layers (you should experiment with different layer numbers and nodes) and N output neurons with an appropriate activation function, start with a linear one.

If you're new to neural networks I'd recommend setting this up using Keras in Python.


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