emukit.multi_fidelity.models package¶
Submodules¶
Contains linear models
- class emukit.multi_fidelity.models.linear_model.GPyLinearMultiFidelityModel(X, Y, kernel, n_fidelities, likelihood=None)¶
Bases:
GP
A thin wrapper around GPy.core.GP that does some input checking and provides a default likelihood
Contains code for non-linear model multi-fidelity model.
It is based on this paper:
Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling. P. Perdikaris, M. Raissi, A. Damianou, N. D. Lawrence and G. E. Karniadakis (2017) https://royalsocietypublishing.org/doi/10.1098/rspa.2016.0751
- emukit.multi_fidelity.models.non_linear_multi_fidelity_model.make_non_linear_kernels(base_kernel_class, n_fidelities, n_input_dims, ARD=False)¶
This function takes a base kernel class and constructs the structured multi-fidelity kernels
At the first level the kernel is simply: .. math
k_{base}(x, x’)
At subsequent levels the kernels are of the form .. math
k_{base}(x, x’)k_{base}(y_{i-1}, y{i-1}’) + k_{base}(x, x’)
- Parameters
base_kernel_class (
Type
[Kern
]) – GPy class definition of the kernel type to construct the kernels atn_fidelities (
int
) – Number of fidelities in the model. A kernel will be returned for each fidelityn_input_dims (
int
) – The dimensionality of the input.ARD (
bool
) – If True, uses different lengthscales for different dimensions. Otherwise the same lengthscale is used for all dimensions. Default False.
- Return type
- Returns
A list of kernels with one entry for each fidelity starting from lowest to highest fidelity.
- class emukit.multi_fidelity.models.non_linear_multi_fidelity_model.NonLinearMultiFidelityModel(X_init, Y_init, n_fidelities, kernels, n_samples=100, verbose=False, optimization_restarts=5)¶
Bases:
IModel
,IDifferentiable
Non-linear Model for multiple fidelities. This implementation of the model only handles 1-dimensional outputs.
The theory implies the training points should be nested such that any point in a higher fidelity exists in all lower fidelities, in practice the model will work if this constraint is ignored.
- set_data(X, Y)¶
Updates training data in the model.
- Parameters
X (
ndarray
) – New training features.Y (
ndarray
) – New training targets.
- Return type
- property X¶
input array of size (n_points x n_inputs_dims) across every fidelity in original input domain meaning it excludes inputs to models that come from the output of the previous level
- Type
return
- property Y¶
output array of size (n_points x n_outputs) across every fidelity level
- Type
return
- property n_samples¶
- predict(X)¶
Predicts mean and variance at fidelity given by the last column of X
Note that the posterior isn’t Gaussian and so this function doesn’t tell us everything about our posterior distribution.
- Parameters
X (
ndarray
) – Input locations with fidelity index appended.- Return type
Tuple
[ndarray
,ndarray
]- Returns
mean and variance of posterior distribution at X.
- get_prediction_gradients(X)¶
Predicts mean and variance and the gradients of the mean and variance with respect to X.
- Parameters
X (
ndarray
) – input location.- Return type
Tuple
[ndarray
,ndarray
]- Returns
(mean, mean gradient, variance, variance gradient) Gradients will be shape (n_points x (d-1)) because we don’t return the gradient with respect to the fidelity index.
- get_f_minimum()¶
Get the minimum of the top fidelity model.
- Return type
ndarray