Design of Experiments

mixle.doe covers the design and analysis loop around expensive black-box functions. It is useful when you cannot evaluate every input, labels are expensive, simulation is slow, or you need to quantify how inputs drive model outputs.

The package is organized around four phases:

1. generate an initial design;

2. fit or query a surrogate;

3. choose follow-up points by acquisition, information gain, or active learning;

4. analyze sensitivity, uncertainty propagation, or calibration.

Design Generators

Design generators return NumPy arrays scaled to supplied bounds.

from mixle.doe import latin_hypercube, sobol_design

bounds = [(0.0, 1.0), (-2.0, 2.0)]

x_lhs = latin_hypercube(bounds, n=16, seed=0)
x_sobol = sobol_design(bounds, n=32)

Available generators include:

• random designs;

• Latin hypercube and maximin Latin hypercube;

• Sobol and Halton sequences;

• MaxPro designs;

• full factorial, fractional factorial, and Plackett-Burman designs;

• central composite and Box-Behnken response-surface designs;

• simplex lattice and simplex centroid mixture designs;

• optimal designs under D, A, I, G, E, and c criteria.

Design Diagnostics

Use diagnostics before spending an expensive run budget:

from mixle.doe import design_diagnostics

report = design_diagnostics(x_lhs)
print(report)

Diagnostics help compare coverage, spacing, and projection behavior across candidate designs.

Bayesian Optimization

The Bayesian optimization layer provides standard single-point acquisitions and batch/high-dimensional variants.

from mixle.doe import minimize

def objective(x):
    return expensive_simulator(x)

result = minimize(
    objective,
    bounds=[(0.0, 1.0), (-2.0, 2.0)],
    n_init=8,
    n_iter=24,
    seed=0,
)

print(result.x_best, result.y_best)

Acquisition functions include expected improvement, log expected improvement, probability of improvement, upper confidence bound, Thompson sampling, and knowledge gradient. Advanced routes include Monte-Carlo q-EI, local penalization, max-value entropy search, trust-region BO, constrained BO, multi-objective BO, and multi-fidelity BO.

Active Learning

Active learning chooses points that most improve a surrogate or parameter estimate.

from mixle.doe import active_learning_design

design = active_learning_design(
    initial_x,
    initial_y,
    bounds=[(0.0, 1.0), (-2.0, 2.0)],
    n_iter=10,
)

Lower-level scoring functions include alm_scores, alc_scores, expected_information_gain_linear, and expected_information_gain_nmc.

Sensitivity Analysis

Sensitivity tools quantify which inputs matter.

from mixle.doe import morris_screening, sobol_indices

morris = morris_screening(model_fn, bounds, n_trajectories=20, seed=0)
sobol = sobol_indices(model_fn, bounds, n=1024, seed=0)

Use Morris screening for a cheaper qualitative pass and Sobol indices when you need variance-based main and interaction effects.

Uncertainty Propagation and Calibration

propagate and unscented_transform push input uncertainty through a model. calibrate implements Kennedy-O’Hagan style calibration to field data.

from mixle.doe import propagate, unscented_transform

propagated = propagate(model_fn, input_distribution, n=1000, seed=0)
approx = unscented_transform(model_fn, mean, cov)

How DOE Connects to Task Distillation

mixle.task uses the same design philosophy for label acquisition. Active distillation treats teacher calls as an expensive experiment and spends the label budget on informative examples. Use Task Distillation for the task-facing workflow.

API Map

Area	Key imports
Space-filling designs	latin_hypercube, sobol_design, halton_design, maxpro_design
Classical designs	full_factorial, fractional_factorial, plackett_burman
Response-surface designs	central_composite, box_behnken, response_surface
Mixture designs	simplex_lattice, simplex_centroid, to_pseudocomponents
Optimal design	optimal_design, available_criteria, d_criterion
Bayesian optimization	minimize, propose_next, propose_batch, BayesianOptimizer
Advanced BO	turbo_minimize, constrained_minimize, multi_minimize
Active learning	active_learning_design, propose_active_learning
Analysis	sobol_indices, morris_screening, propagate, calibrate

Detailed API Inventory

Area	Imports
Bounds and random designs	Bounds, random_design, maximin_latin_hypercube
Factorial analysis	factorial_effects, FactorialEffects, polynomial_features
Response surfaces	ResponseSurface, OptimizationResult
Acquisition functions	expected_improvement, knowledge_gradient, propose_knowledge_gradient, log_expected_improvement, probability_of_improvement, upper_confidence_bound, thompson_sampling
Acquisition registry	register_acquisition, available_acquisitions
Optimal-design criteria	a_criterion, i_criterion, g_criterion, e_criterion, c_criterion, register_criterion
Constrained BO	ConstrainedBayesOptResult, probability_of_feasibility, propose_next_constrained
Multi-objective and batch BO	MultiObjectiveResult, pareto_mask, monte_carlo_qei, propose_qei_batch, propose_local_penalization
Entropy and trust-region BO	BayesOptResult, max_value_entropy_search, sample_max_values, propose_mes, TrustRegion
Multi-fidelity and sensitivity	multi_fidelity_minimize, fast_indices, dgsm
Propagation and calibration	register_propagator, KOCalibration