JetGP Module Examples

This section provides examples for using JetGP classes, including DEGP, WDEGP, DDEGP, GDDEGP, and WDDEGP.

Tutorials

• Derivative-Enhanced Gaussian Process (DEGP)
  • Overview
  • Example 1: 1D First-Order Derivatives Only
  • Example 2: 1D First- and Second-Order Derivatives
  • Example 3: 2D First-Order Derivatives
  • Example 4: 2D Second-Order (Main) Derivatives
  • Example 5: 1D Heterogeneous Derivative Coverage
  • Example 6: Predicting Untrained Partial Derivatives
  • Example 7: 2D Function-Only Training with Derivative Predictions
• 1D DEGP Kernel Comparison
  • Overview
  • Step 1: Import packages and define training data
  • Step 2: Squared Exponential (SE) kernel
  • Step 3: Matern kernel
  • Step 4: Rational Quadratic (RQ) kernel
  • Step 5: Sine-Exponential (SineExp) kernel
  • Step 6: Visual comparison – function predictions
  • Step 7: Visual comparison – derivative predictions
  • Step 8: RMSE summary
  • Summary
• 2D DEGP Kernel Comparison: Isotropic vs Anisotropic
  • Overview
  • Step 1: Define the Franke function and its derivatives
  • Step 2: Generate training and test data
  • Step 3: Train all 8 kernel variants
  • Step 4: RMSE summary table
  • Step 5: Visual comparison – surface predictions
  • Step 6: Error heatmaps
  • Summary
• Directional Derivative-Enhanced Gaussian Process (DDEGP)
  • Overview
  • Example 1: Global Directional GP on the Branin Function
• Directional Derivative-Enhanced Gaussian Process (DDEGP) - Selective Coverage
  • Overview
  • Example 2: Selective Derivative Coverage with Global Ray Basis
  • Example 3: Predicting Along an Untrained Ray Direction
  • Example 4: 2D Function-Only Training with Derivative Predictions
• Generalized Directional Derivative-Enhanced Gaussian Process (GDDEGP)
  • Overview
  • Example 1: Generalized Directional GP with Gradient-Aligned Rays on the Branin Function
• Example 2: GDDEGP with Multiple Directional Derivatives Per Point Using Global Perturbations
  • Overview
• GDDEGP Tutorial: Mixed Derivative Coverage
  • Overview
  • Data Structure Correspondence
  • Step 1: Import required packages
  • Step 2: Set configuration parameters
  • Step 3: Define the Branin function
  • Step 4: Generate training data with MIXED derivative coverage
  • Step 5: Initialize and train the GDDEGP model
  • Step 6: Evaluate model on a test grid
  • Step 7: Verify interpolation at training points
  • Step 8: Visualize results with mixed coverage
  • Summary
  • Key Takeaways
  • Example 3: More Direction Types Than Spatial Dimensions
  • Example 4: 2D Function-Only Training with Derivative Predictions
• Weighted Derivative-Enhanced Gaussian Process (WDEGP)
  • Weighted Individual Submodel Framework
  • Key Data Structures: submodel_indices and derivative_specs
  • Derivative Predictions
  • Example 1: 1D Weighted DEGP with Individual Submodels
  • Example 2: 1D Sparse Weighted DEGP with Selective Derivative Observations
  • Example 3: 1D Weighted DEGP with Multiple Submodels
  • Example 4: Heterogeneous Derivative Indices Within Submodels
  • Example 5: WDEGP with Different Derivative Specifications per Submodel
  • Example 6: WDEGP with DDEGP Submodels (Global Directional Derivatives)
  • Example 7: WDEGP with GDDEGP Submodels (Point-Wise Directional Derivatives)
  • Example: Predicting Derivatives Not Common to All Submodels
  • Example 8: 2D Function-Only WDEGP with Derivative Predictions