The MultiOutputGP Class

Implementation of a multiple-output Gaussian Process Emulator.

Essentially a parallelized wrapper for the predict method. To fit in parallel, use the fit_GP_MAP routine

Required arguments are inputs and targets, both of which must be numpy arrays. inputs can be 1D or 2D (if 1D, assumes second axis has length 1). targets can be 1D or 2D (if 2D, assumes a single emulator and the first axis has length 1).

Optional arguments specify how each individual emulator is constructed, including the mean function, kernel, priors, and how to handle the nugget. Each argument can take values allowed by the base GaussianProcess class, in which case all emulators are assumed to use the same value. Any of these arguments can alternatively be a list of values with length matching the number of emulators to set those values individually.

Additional keyword arguments include inputdict, and use_patsy, which control how strings are parsed to mean functions, if using.

class mogp_emulator.MultiOutputGP.MultiOutputGP(inputs, targets, mean=None, kernel=<mogp_emulator.Kernel.SquaredExponential object>, priors=None, nugget='adaptive', inputdict={}, use_patsy=True)

Implementation of a multiple-output Gaussian Process Emulator.

Essentially a parallelized wrapper for the predict method. To fit in parallel, use the fit_GP_MAP routine

Required arguments are inputs and targets, both of which must be numpy arrays. inputs can be 1D or 2D (if 1D, assumes second axis has length 1). targets can be 1D or 2D (if 2D, assumes a single emulator and the first axis has length 1).

Optional arguments specify how each individual emulator is constructed, including the mean function, kernel, priors, and how to handle the nugget. Each argument can take values allowed by the base GaussianProcess class, in which case all emulators are assumed to use the same value. Any of these arguments can alternatively be a list of values with length matching the number of emulators to set those values individually.

Additional keyword arguments include inputdict, and use_patsy, which control how strings are parsed to mean functions, if using.

__init__(inputs, targets, mean=None, kernel=<mogp_emulator.Kernel.SquaredExponential object>, priors=None, nugget='adaptive', inputdict={}, use_patsy=True)

Create a new multi-output GP Emulator

predict(testing, unc=True, deriv=True, include_nugget=True, processes=None)

Make a prediction for a set of input vectors

Makes predictions for each of the emulators on a given set of input vectors. The input vectors must be passed as a (n_predict, D) or (D,) shaped array-like object, where n_predict is the number of different prediction points under consideration and D is the number of inputs to the emulator. If the prediction inputs array has shape (D,), then the method assumes n_predict == 1. The prediction points are passed to each emulator and the predictions are collected into an (n_emulators, n_predict) shaped numpy array as the first return value from the method.

Optionally, the emulator can also calculate the uncertainties in the predictions (as a variance) and the derivatives with respect to each input parameter. If the uncertainties are computed, they are returned as the second output from the method as an (n_emulators, n_predict) shaped numpy array. If the derivatives are computed, they are returned as the third output from the method as an (n_emulators, n_predict, D) shaped numpy array. Finally, if uncertainties are computed, the include_nugget flag determines if the uncertainties should include the nugget. By default, this is set to True.

As with the fitting, this computation can be done independently for each emulator and thus can be done in parallel.

Parameters:
  • testing (ndarray) – Array-like object holding the points where predictions will be made. Must have shape (n_predict, D) or (D,) (for a single prediction)
  • unc (bool) – (optional) Flag indicating if the uncertainties are to be computed. If False the method returns None in place of the uncertainty array. Default value is True.
  • deriv (bool) – (optional) Flag indicating if the derivatives are to be computed. If False the method returns None in place of the derivative array. Default value is True.
  • include_nugget (bool) – (optional) Flag indicating if the nugget should be included in the predictive variance. Only relevant if unc = True. Default is True.
  • processes (int or None) – (optional) Number of processes to use when making the predictions. Must be a positive integer or None to use the number of processors on the computer (default is None)
Returns:

Tuple of numpy arrays holding the predictions, uncertainties, and derivatives, respectively. Predictions and uncertainties have shape (n_emulators, n_predict) while the derivatives have shape (n_emulators, n_predict, D). If the do_unc or do_deriv flags are set to False, then those arrays are replaced by None.
Return type:

tuple