Prediction based on Kriging with EA-evolving Hyperparameters

This script demonstrates the use of Kriging for prediction, with hyperparameters optimized using an Evolutionary Algorithm (EA).

% This script code aims to help my graduates to make sense of the prediction surrogate based on Kriging model( or Guassian model), which

% demonstrates the use of Kriging for prediction, with hyperparameters optimized using an Evolutionary Algorithm (EA).

% The first edition is finished by Chixin Xiao, on 17 Nov 2024, Changsha, China

% Email: [e-mail]

% Synthetic Data Generation: X_samples = -5 + 10 * rand(num_samples, 2).

% Data Splitting: Divides data into training and testing sets with an 80-20 split.

% Model Training: Trains Kriging models for each output variable (X_samples and y_samples) using a hypothetical function train_kriging.

% Prediction Calculation: Computes predictions and error metrics.

% Plotting: Shows:

% Known y_test vs. predicted values y_pred, helping visualize the fit.

% Error curves for y_test and y_pred, with 'Prediction Error' displayed in the title.

% Objective Function: Calculates minimun -log_likelihood (i.e., maximum log_likelihood) based on the predicted values for the given data.

% Evolutionary Algorithm:

% 1)Initializes a random population (hyperparameters population).

% 2)Iterates through selection, crossover, and mutation.

% 3)Keeps best solutions after each generation.

% Kriging Model Prediction:

% Uses optimized hyperparameters to make predictions on test data.

% visualizes results.