Predict Aircraft Noise Levels with Neural Networks

Download the Airfoil Self-Noise dataset from the UCI Machine Learning Repository. The five input features are: frequency (Hz), angle of attack (degrees), chord length (meters), free-stream velocity (m/s), and suction side displacement thickness (meters). The target is scaled sound pressure level (dB).

Load the data into pandas and compute summary statistics. Plot the target (SPL) against each feature individually using scatter plots. You should see clear trends: SPL generally increases with velocity (noise scales roughly as V⁵ for trailing edge noise) and shows a complex relationship with angle of attack and frequency. The displacement thickness encodes boundary layer state, which strongly influences noise generation.

Normalize all features and the target using StandardScaler — neural networks train much faster when inputs are centered and scaled. Split into train (70%), validation (15%), and test (15%) sets. Convert to PyTorch tensors and wrap in DataLoader objects with a batch size of 32–64.

Create a baseline: train a scikit-learn linear regression on the same splits and record its test RMSE and R². This gives you a floor to beat with the neural network. Also try a polynomial regression (degree 2) — the V⁵ power law suggests non-linear features will help even without deep learning.

Define a feedforward network in PyTorch: 5 input features → 64 hidden units → 128 hidden units → 64 hidden units → 1 output. Use ReLU activation between layers. Initialize with the default PyTorch initialization (Kaiming uniform).

Write a custom training loop: for each epoch, iterate over batches from the training DataLoader, compute MSE loss, backpropagate, and update weights with Adam optimizer (lr=1e-3). After each epoch, evaluate on the validation set without gradient computation. Print train and validation loss every 10 epochs. Train for 200–500 epochs.

If the validation loss is significantly higher than training loss, you are overfitting. Add dropout (0.1–0.3) after each hidden layer and weight decay (1e-4 to 1e-3) to the Adam optimizer. Try adding batch normalization before the activation functions.

Experiment systematically: vary the number of layers (2–5), hidden units (32–256), learning rate (1e-2 to 1e-4), and dropout rate. Use a simple grid or random search — document each experiment's validation RMSE in a table. A good model should achieve R² > 0.90 on the test set; with careful tuning, R² > 0.95 is achievable.

Plot predicted vs. actual SPL on the test set. Identify any systematic biases — does the model under-predict at high SPL or over-predict at low frequencies? Plot residuals (errors) against each input feature to check for patterns. If residuals correlate with a specific feature, consider adding that feature's higher-order terms or transformations.

Compute the model's test RMSE in decibels. In aeroacoustics, a prediction error below 2–3 dB is generally considered useful for design purposes. Compare your neural network's accuracy to the linear and polynomial baselines — how much did the non-linearity of the neural network buy you?

Use the trained model to explore aeroacoustic trends. Fix all inputs except free-stream velocity and sweep it from 30 to 70 m/s — plot the predicted SPL. Does the model learn the expected velocity power law? Similarly, sweep angle of attack and frequency to check if the predictions match known acoustic behavior.

Try feature ablation: retrain the model with one feature removed at a time and observe which omission hurts accuracy the most. This tells you which physical parameter is most important for noise prediction — you should find that velocity and displacement thickness dominate, matching aeroacoustic theory. Write up a discussion connecting the ML results to the physics of trailing edge noise generation.