neural network to match image

Question

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!

Answer 1

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

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:

• Inverse Design of Airfoil Using a Deep Convolutional Neural Network
• Application of Convolutional Neural Network to Predict Airfoil Lift Coefficient
• Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows

You can inspire your models architecture by theirs

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

Answer 2

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.