Add GPR functions and unit tests

[vtommasini]

Partial merge of GPR Library, adding only the self contained ML class and functions for now (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 test is included for sanity checks

[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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[Copilot]

The learning rate value 0.05 is a magic number that should be extracted as a named constant or parameter for better maintainability and easier tuning.

[Copilot]

Missing space after comma in reshape(-1,1). Should be reshape(-1, 1) per PEP 8 style guidelines.

Suggested change

	X = np.linspace(0, 2 * np.pi, n).reshape(-1,1)
	X = np.linspace(0, 2 * np.pi, n).reshape(-1, 1)

[Copilot]

Missing space after comma in train_gpr_model(X,Y). Should be train_gpr_model(X, Y) per PEP 8 style guidelines.

Suggested change

	model, likelihood = train_gpr_model(X,Y)
	model, likelihood = train_gpr_model(X, Y)

[Copilot]

The function list in the header comment (lines 7-24) lists 16 functions, but only 4 are actually present in this file (GPRegressionModel class, train_gpr_model, predict_with_gpr_model, run_gpr_pipeline). This documentation is misleading and should be updated to reflect only the functions that are actually implemented.

Suggested change

	# contains all functions necessary to run the GPR Model
	# used to predict better low-eccentricity orbital parameter initial guesses
	# functions:
	# 1. normalize_data
	# 2. denormalize_predictions
	# 3. omega_and_adot
	# 4. omegaAndAdot
	# 5. polynomial_fit_with_confidence
	# 6. GPRegressionModel (class)
	# 7. train_gpr_model
	# 8. predict_with_gpr_model
	# 9. run_gpr_pipeline
	# 10. train_model_and_eigenvalue_analysis
	# 11. loo_predictions
	# 12. parse_test_runs
	# 13. apply_gpr_corrections
	# 14. save_gpr_corrected
	# 15. loo_crossval
	# 16. plot_loo_residuals
	# Contains functions and classes necessary to run the GPR Model
	# used to predict better low-eccentricity orbital parameter initial guesses
	# Implemented functions/classes:
	# - GPRegressionModel (class)
	# - train_gpr_model
	# - predict_with_gpr_model
	# - run_gpr_pipeline

[Copilot]

The plot parameter in the docstring is missing a type annotation. Should be plot (bool): Whether to produce correlation plots. for consistency with other parameters.

Suggested change

	plot: whether to produce correlation plots.
	silent: whether to suppress print statements entirely.
	plot (bool): Whether to produce correlation plots.
	silent (bool): Whether to suppress print statements entirely.

[Copilot]

The magic number 0 for the random seed should be extracted as a named constant (e.g., RANDOM_SEED = 0) at the class or module level for better maintainability and clarity.

[Copilot]

Missing space after comma in train_gpr_model(X,Y). Should be train_gpr_model(X, Y) per PEP 8 style guidelines.

[Copilot]

Inconsistent spacing around = in keyword arguments. Should be ard_num_dims=input_dim (no spaces) per PEP 8 style guidelines.

Suggested change

	self.rbf_kernel = gpytorch.kernels.RBFKernel(ard_num_dims = input_dim)
	self.rbf_kernel = gpytorch.kernels.RBFKernel(ard_num_dims=input_dim)

[Copilot]

Import of 'pd' is not used.

Suggested change

import pandas as pd

[Copilot]

Import of 'argparse' is not used.

Suggested change

import argparse