GP-DNN

Hierarchical Gaussian process and neural network regression. Python code for training multivariate GP-DNNs using tensorflow and tensorflow-probability (see requirements.txt file). Refer to paper by Pradhan et al. (2023) referenced below for description of methodology and application.

The package contains the following:

• gp_dnn_hyper_tuning.py: Python file to perform hyper-parameter tuning of GP-DNN models. User needs to specify the following inside the file:

  • head_dir: Local directory to save hyper-parmaeter trained model outputs
  • data_dir: Local data directory
  • training_file_name: Name of pickle file containing training data. For data structure, see file.
  • num_samp: No. of experiments for hyper-parameter tuning
  • num_epochs: No. of epoch for DNN training
  • num_coef: No of variables for multivariate GP. Note name coef in code is used to denote variables/coefficients while name var denotes variance.
  • Need to specify max and min ranges of several hyper-parameters Given these specification, the file calls gp_dnn_hyper_tuning(...) defined inside gp_dnn_hyper_tuning.py for training the GP-DNN

• gp_dnn_training.py: Contains function gp_dnn_training for training the GP-DNN.

  • Requires the training data, # of epochs, model output path and hyper-parameters
  • Saves following Tensorflow outputs in provided output path
    • Model weights saved as model checkpoints, see TF documentation
    • Training history in a history.pickle
    • Model hyper-parameters and training metrics in a params.json file

• utils_gp_dnn.py: Contains the following:

  • GP_DNN_marginal_neglikelihood_loss: TF subclass for GP-DNN marginal likelihood loss functions
  • GP_DNN_likelihood: TF subclass for GP-DNN likelihood metric
  • GP_DNN_RMSE: TF subclass for GP-DNN mean RMSE metric
  • cokriging_covariance: Function for constructing covariance matrix using Matérn kernels

Users may choose the best model from hyper-parameter tuning based on saved metrics and perform subsequent analyses

Reference:

• Pradhan, A., Adams, K. H., Chandrasekaran, V., Reager, J. T., Liu, Z., Stuart, A. M., Turmon, M. J., (2023), Modeling groundwater levels in California’s Central Valley by hierarchical Gaussian process and neural network regression, arXiv:2310:14555v1 [physics.geo-ph] [arXiv]