Add GPR functions and unit tests

[vtommasini]

Partial merge of the Gaussian Process Regression (GPR) Library for predicting the radial expansion rate and radial velocity of BBH simulations, currently consisting only of the self contained ML class and functions (no eccentricity control related functions).

Contains the following:

1. Model class, handles input data setup with initialization, normalization, and denormalization functions
2. GPR model training function, which stores normalization statistics
3. Prediction function, which returns the mean and uncertainty
4. GPR pipeline, which encompasses training, prediction, plots, and output metrics

Unit tests covering training, prediction, normalization/denormalization, and pipeline functionality using synthetic sine wave data are included for sanity check.

[Copilot]

Pull request overview

This PR adds a Gaussian Process Regression (GPR) machine learning library for predicting orbital parameters, consisting of a self-contained model class with normalization capabilities and associated training/prediction functions. The implementation includes comprehensive unit tests to validate functionality.

• GPR model implementation with mixed RBF and Matern kernels, linear mean function, and input/output normalization
• Training and prediction functions with stored normalization parameters
• Complete pipeline function for training, prediction, visualization, and metrics reporting

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 17 comments.

File	Description
GPR_library.py	Implements GPRegressionModel class, training function with Adam optimizer and learning rate scheduling, prediction function with denormalization, and full pipeline with plotting capabilities
TestGPRLibrary.py	Provides comprehensive unit tests covering training, prediction, normalization/denormalization, and pipeline functionality using synthetic sine wave data

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[nilsvu]

Very nice code and useful tests, the comments are very helpful 👍 please fix these minor comments and also address the copilot review above.

[nilsvu]

Looks good. Please fix the few unresolved comments above. In particular, please explain the magic numbers. You can add comments explaining how you chose them, and give an idea how much you have tested different numbers. The idea is to give people editing the code an idea if these are finely tuned numbers that should not be touched, or barely explored at all and open for experimentation.

Then please squash all of your commits into one.

[nilsvu]

Please squash your commit into one (including these changes). Please also rebase on the latest main branch, as the test you added wasn't run by GitHub. It will run automatically once you rebased.

[nilsvu]

The automated tests run now and pass 👍 Merging this now so we can move on with the next PRs. We can clarify or fix the question below in a follow-up (probably best to make the number of training iterations an input parameter with a default).