bayesvalidrox.surrogate_models.sequential_design.SequentialDesign

class bayesvalidrox.surrogate_models.sequential_design.SequentialDesign(meta_model, exp_design, discrepancy, observations=None, parallel=False, out_names=None, verbose=False)

Bases: object

Contains options for choosing the next training sample iteratively.

Parameters

meta_modelobj

A bvr.MetaModel object. If no MetaModel should be trained and used, set this to None.

modelobj

A model interface of type bvr.PyLinkForwardModel that can be run.

exp_designobj

The experimental design that will be used to sample from the input space.

discrepancyobj

A bvr.Discrepancy object that describes the model uncertainty, i.e. the diagonal entries of the variance matrix for a multivariate normal likelihood.

parallelbool, optional

Set to True if the evaluations should be done in parallel. The default is False.

out_nameslist, optional

The list of requested output keys to be used for the analysis. The default is None.

verbosebool, optional

Verbosity of the methods, the default is False.

__init__(meta_model, exp_design, discrepancy, observations=None, parallel=False, out_names=None, verbose=False)

Methods

__init__(meta_model, exp_design, discrepancy)
choose_next_sample()	Runs optimal sequential design.
dual_annealing(exploit_method, bounds, run_idx)	Exploration algorithm to find the optimum parameter space.
run_exploitation(all_candidates)	Run the selected exploitation method.
tradeoff_weights(tradeoff_scheme, old_ed_x, ...)	Calculates weights for exploration scores based on the requested scheme: None, equal, epsilon-decreasing and adaptive.
util_alph_opt_design(all_candidates)	Enriches the Experimental design with the requested alphabetic criterion based on exploring the space with number of sampling points.
util_bayesian_active_design(x_can)	Computes score based on Bayesian active design criterion (var).
util_var_opt_design(x_can)	Computes the exploitation scores based on:

choose_next_sample()

Runs optimal sequential design.

Raises

NameError

Wrong utility function.

Returns

Xnewarray (n_samples, n_params)

Selected new training point(s).

dual_annealing(exploit_method, bounds, run_idx, verbose=False)

Exploration algorithm to find the optimum parameter space.

Note: Currently does not support BayesActDesign due to possibility of inf/nan values.

Parameters

exploit_methodstring

Exploitation method: VarOptDesign

boundslist of tuples

List of lower and upper boundaries of parameters.

run_idxint

Run number.

verbosebool, optional

Print out a summary. The default is False.

Returns

run_idxint

Run number.

array

Optimial candidate.

run_exploitation(all_candidates)

Run the selected exploitation method. Supports ‘bayesactdesign’, ‘varoptdesign’ and ‘alphabetic’.

Parameters

all_candidatesnp.ndarray

Candidate samples.

Returns

norm_score_exploitationnp.ndarray

Exploitation scores

opt_typestr

Optimization type, either ‘minimization’ or ‘maximization’

tradeoff_weights(tradeoff_scheme, old_ed_x, old_ed_y)

Calculates weights for exploration scores based on the requested scheme: None, equal, epsilon-decreasing and adaptive.

exploit_only: No exploration, full exploitation. explore_only: Full exploration, no exploitation. equal: Same weights for exploration and exploitation scores. epsilon-decreasing: Start with more exploration and increase the

influence of exploitation along the way with an exponential decay function

adaptive: An adaptive method based on:

Liu, Haitao, Jianfei Cai, and Yew-Soon Ong. “An adaptive sampling approach for Kriging metamodeling by maximizing expected prediction error.” Computers & Chemical Engineering 106 (2017): 171-182.

Parameters

tradeoff_schemestring

Trade-off scheme for exloration and exploitation scores.

old_ed_xarray (n_samples, n_params)

Old experimental design (training points).

old_ed_ydict

Old model responses (targets).

Returns

exploration_weightfloat

Exploration weight.

exploitation_weight: float

Exploitation weight.

util_alph_opt_design(all_candidates)

Enriches the Experimental design with the requested alphabetic criterion based on exploring the space with number of sampling points.

Ref: Hadigol, M., & Doostan, A. (2018). Least squares polynomial chaos expansion: A review of sampling strategies., Computer Methods in Applied Mechanics and Engineering, 332, 382-407.

Arguments

all_candidatesarray

Array with candidate points to be searched

Returns

scoresarray of shape (n_candidates,)

The scores for each candidate point based on the selected utility function.

util_bayesian_active_design(x_can)

Computes score based on Bayesian active design criterion (var).

It is based on the following paper: Oladyshkin, Sergey, Farid Mohammadi, Ilja Kroeker, and Wolfgang Nowak. “Bayesian3 active learning for the gaussian process emulator using information theory.” Entropy 22, no. 8 (2020): 890.

Parameters

x_cannp.ndarray

A single candidate sample.

Returns

float

Exploitation score for the candidate sample.

util_var_opt_design(x_can)

Computes the exploitation scores based on:

ALM (Active Learning MacKay):

Selects points where the surrogate model’s predictive variance is largest.

EIGF (Expected Improvement for Global Fit):

Selects points where the prediction error (vs. nearest observed data) plus the variance is largest.

MI (Mutual Information):

Selects points that maximize mutual information between the new sample and the unobserved.

ALC (Active Learning Cohn):

Selects candidate points that minimize the average predictive variance across a set of Monte Carlo evaluation points.

The calculations are based on the following sources. ALM:

MacKay, D. J. (1992). Information-based objective functions for active data selection. Neural computation

EIGF, MI, ALC:

Beck, J., & Guillas, S. (2016). Sequential design with mutual information for computer experiments (MICE): Emulation of a tsunami model. SIAM/ASA Journal on Uncertainty Quantification

Parameters

x_canarray of shape (n_samples, n_params)

Candidate samples.

Returns

float

Score.