Inverse design of airfoil with DL methods

1. Task description and problem setting

Task: to create airfoil with required aerodynamical parameters.

Problem: there is good XFoil tool for analysis of existing airfoil, but there is no tool, which can create arbitrary airfoil by known aerodynamical parameters.

Foil looks like:

parameters looks like:

So we can get parameters from foil picture but can not get new foil from required parameters.

2. Solution approach

Let's do like we usually do in DL: take some "black box", put known data "X" to the input, put desired data "y" to the output and run a training.

What do we want from this "black box?" New airfoil picture. So our "y" data will be foils images:

Now we can take key airfoil parameters and use as "X" data. What are requirements for this data?

• it shall be unique for each foil;
• it shall be full enough to describe airfoil;
• there shall be quite large and multidimensional array of such data to allow "black box" be successfully trained.

Such parameters are:

• Cl: lift coefficient;
• Cd: drag coefficient;
• Cm: moment coefficient;
• Cp: pressure coefficient;
• d: foil thickness at flap root;
• S: foil max thickness.

As soon as foil parameters are unique for each combination of Re and Alpha (except S and d), we easily get 3D array of "X" data:

• axis 0: required parameters for particular Re and Alpha;
• axis 1: Re;
• axis 2: Alpha:

What are Re and Alpha?!!

Re:

In fact, it is proportional to airflow speed, because all other variables are fixed in our approach.

Alpha:

---

Resulting array looks like:

Layers 6 and 7 with Re and Alpha will not take part in predictions; they need for info transfer between modules and can be dropped or replaced with some additional foil parameters.

So, now we have "X" data as an array of (n_data_layers, n_points_Re, n_points_alfa) shape.

3. Implementation

For check of this data approach let's take extracting part of U-net and train it on images of 512x512 size.

ToDo:

1. Change image size to 256x1024 and achieve the same or better results. - COMPLETED
2. Use more complicated CNN architectures.
3. Implement ensemble of different CNNs.

4. Loss and Metrics

Now using simplest MSE both for metric and loss.

ToDo:

1. Use Tversky loss function and add IoU metric. - COMPLETED

5. Production use

Backend implemented as a microservice, based on a Flask server.

Frontend implemented as Excel VBA macros, interacting with the server via HTTP requests. Why Excel?

• potential tool users are not experienced PC users and Excel is the maximum of their knowledge;
• large tables with input data require complicated frontend;
• Excel gives flexibility in adding new modules like graphs and charts.

6. Predictions test

Let's try to predict airfoil with known geometry by its parameters.

This is input array for Cl:

This is prediction result before rounding, smoothing and interpolation:

And here is smoothed interpolated prediction result, compared with true foil: