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Design of Experiment

What is the Design of Experiment

Design of Experiment (DoE) refers to a structured, strategic approach for selecting samples withing decision space to efficiently system's behavior. DoE aims to extract the the maximum amount of information with a minimal number of experiments or simulations. Therefore, DoE methods are the essential for uncertainty quantification, optimization, or surrogate modeling.

Overview of UQPyL.DoE module

The DoE module of UQPyL provides several design of experiments methods to meet various user requirements.


DoE methods include:

  • Full Factorial Designs (FFD): FFD would explore all possible combinations of factors at different levels.

  • Latin Hypercube Sampling (LHS): LHS is designed to obtain uniform and efficient coverage of decision space with fewer samples. DoE module provides multiple variants of LHS, e.g., classic, center, maximin, center_maximin, correlation.

  • Monte Carlo Sampling: Random sampling is the most basic method. Each sample is selected independently from the specified probability distributions.

  • Sobol Sequence: This method is a quasi-random low-discrepancy sequence designed to uniformly fill the parameter space more effectively than purely random methods.

  • Saltelli Sequence: It is a variant of Sobol Sequence, more suitable for variance-based global sensitivity analysis.

  • Morris Sequence: This method is designed for Morris Method in sensibility analysis.

All methods in UQPyL.DoE module inherits from SamplerABC. Here, we give the API reference of SamplerABC:


Class SamplerABC:

The SamplerABC is the base class for DoE methods in UQPyL. It provides a unified sample function that allows users to generate samples efficiently.

Constructor: 

__init__

- Description:

Initializes a new instance of DoE method.

Note: The hyper-parameters vary between different DoE methods. Please refer to each specific method for details.

For example, the __init__ method of LHS accepts criterion('classic', 'center' ... 'correlated') and iterations (if required) as input arguments.

Method:

sample

- Description:

Generate samples from the decision space.

There are two modes of operation:

1. If no `problem` is provided:
   - The function uses `nt` (number of samples) and `nx` (number of variables)
     to generate samples in the normalized space [0, 1]^nx.

2. If a `problem` is provided:
   - The function uses `nt` and `problem.nInput` to generates samples. 
     And samples would be normalized to the variable bounds 
     defined by the `problem` instance.

- Parameters:
    - nt(int): The parameters would determine the sampling number of each method.
    - nx(int): The dimensions of sampling, optional. Default: None.
    - problem(Problem): The Problem instance defined, optional. Default: None.

- Returns:
    - np.2darray: A 2D Numpy Array of generated array.

    - The number of rows typically corresponds to `nt`, 
      such as in LHS and Random sampling methods.
    - For some methods like Sobol or Saltelli sequences, 
      the number of rows may differ due to internal padding requirements.

How to obtain samples

# Step 1 : Create an instance of DoE method
from UQPyL.DoE import LHS

# Use classic LHS method
lhs = LHS(criterion = "classic") 

# Step 2: Generate a unit sample set with 100 samples in 10 dimensions
# the shape is (nt, nx)
X = lhs.sample(nt = 100, nx = 10)

# Optional: Provide a problem definition to scale the samples accordingly
from UQPyL.problems.single_objective import Sphere

problem = Sphere(nInput = 10)

# Samples are now generated within the bounds defined by the `problem`
# the shape is (nt, problem.nInput)
X = lhs.sample(nt = 100, problem = problem)