ensemble_gaussian

Gaussian control perturbations: ensemble estimates of the gradient, the Hessian and the sensitivity used by SmcOpt.

GaussianEnsemble

Bases: EnsembleOptimizationBase

Gaussian Ensemble class for ensemble-based optimization.

Methods:

Name	Description
gradient	Ensemble gradient
hessian	Ensemble hessian
calc_ensemble_weights	Calculate weights used in sequential monte carlo optimization

__init__(options, simulator, objective)

Parameters:

Name	Type	Description	Default
options	dict	Options for the ensemble class disable_tqdm: supress tqdm progress bar for clean output in the notebook ne: number of perturbations used to compute the gradient state: name of state variables passed to the .mako file prior_: the prior information the state variables, including mean, variance and variable limits num_models: number of models (if robust optimization) (default 1) transform: transform variables to [0,1] if true (default true) natural_gradient: use natural gradient if true (default false)	required
simulator	callable	The forward simulator (e.g. flow)	required
objective	callable	The objective function (e.g. npv)	required

calc_ensemble_weights(x, *args, **kwargs)

Calculate weights used in sequential monte carlo optimization. Updated version that accommodates new base class changes.

Parameters:

Name	Type	Description	Default
x	ndarray	Control vector, shape (number of controls, )	required
args	tuple	Inflation factor, covariance (\(C_x\), shape (number of controls, number of controls)) and survival factor	()

Returns:

Type	Description
sens_matrix, best_ens, best_func : tuple	The weighted ensemble, the best ensemble member, and the best objective function value

gradient(x, *args, **kwargs)

Estimate the ensemble gradient (EnOpt) at a given state.

Parameters:

Name	Type	Description	Default
x	ndarray	Control vector, shape (number of controls, ).	required
args	tuple	First positional argument must be the covariance matrix with shape (number of controls, number of controls).	()

Returns:

Type	Description
ndarray	Ensemble gradient, shape (number of controls, ).

Raises:

Type	Description
ValueError	If required inputs are missing or have invalid shapes.

hessian(x=None, *args, **kwargs)

Ensemble-based Hessian.

Parameters:

Name	Type	Description	Default
x	ndarray	Control vector, shape (number of controls, ). If None, use the last x used in gradient. If x is not None and it does not match the last x used in gradient, recompute the gradient first.	None
args	tuple	Additional arguments passed to function	()

Returns:

Name	Type	Description
hessian	ndarray	Ensemble hessian, shape (number of controls, number of controls)

References

Zhang, Y., Stordal, A.S. & Lorentzen, R.J. A natural Hessian approximation for ensemble based optimization. Comput Geosci 27, 355–364 (2023). https://doi.org/10.1007/s10596-022-10185-z