Optimize Uncertainty with GPR Model and Gekko

Optimization Under Uncertainty: Gaussian Process Regression (GPR) and Gekko Optimization

This video walks through the process of setting up, training, and optimizing a GPR model to handle uncertainty in predictions, ideal for tasks requiring uncertainty-aware decision-making.

Outline:
1. Introduction to Gaussian Process Regression (GPR)
Understanding GPR as a probabilistic model
Benefits of GPR in making predictions with well-defined uncertainty
Detailed mathematical description available in the "Machine Learning for Engineers" course

2. Setting Up the Environment
Importing essential libraries: NumPy, Matplotlib, Gekko, and Scikit-learn's Gaussian Process Regressor and kernels
Installation guide for Gekko if not already installed

3. Data Generation and Visualization
Generating noisy data samples
Visualizing true functions and measured data points

4. Data Preparation
Splitting data into training and testing sets using scikit-learn’s `train_test_split`

5. GPR Model Training
Creating and training a GPR model
Evaluating model performance using the R-squared metric

6. Model Visualization
Plotting trained GPR model predictions and confidence intervals against true functions and noisy measurements

7. Optimization with Gekko
Using Gekko to perform optimization
Minimizing predicted values and uncertainties using the trained GPR model

8. Uncertainty Optimization
Minimizing uncertainty with Gekko

9. Multi-Objective Optimization
Minimizing both expected values and uncertainties as a weighted sum

10. Results Visualization
Visualizing optimization results
Highlighting points of optimized predicted values and uncertainties

Check out the detailed mathematical description on the Gaussian Process Regression learning page in the "Machine Learning for Engineers" course for more insights. Code Blocks Available:

Import Libraries
Generate Data
Data Preparation
GPR Model Training
Model Visualization
Optimization with Gekko
Uncertainty Optimization
Multi-Objective Optimization
Results Visualization