neural network to match image 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!
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.