In this case the true underlying function HyGP had to approximate is the 2D Branin-Hoo function (Viana and Haftka 2009):
BUILDING DATA SET:
30-point Optimal Latin Hypercube DoE in [-5, 10] x [0, 15]
Available here: braninhoo_input_file
VALIDATION DATA SET:
1369-point Full Factorial DoE [-6.5 : 0.5 : 11.5] x [-1.5 : 0.5 : 16.5]
Available here: braninhoo_test_dataset
HyGP hyperparameters (see braninhoo_input_file):
Population size: 200
Primitives: +, -, *, / (protected), ^2, ^3, sin, cos, exp
The experiment done with 10 random initial guesses for numerical coefficients (10-guesses approach) returned as best model the following symbolic expression:
characterised by a coefficient of determination R2=1 on the validation data. The returned expression is as a matter of fact the original underlying Branin-Hoo function, if minor errors on the numerical coefficients are neglected.
In the video below the evolution leading to the correct identification of the Branin-Hoo function is shown:
- F.A.C. Viana and R.T. Haftka. Cross validation can estimate how well prediction variance correlates with error. AIAA Journal, 47(9):2266–2270, 2009.