Latin Hypercube Sampling

Utilize Latin Hypercube Sampling (LHS) to perform random model explorations for experiment design. In this analysis, set <AnalysisType>LHS</AnalysisType>. For example, The following input will utilize LHS to generate 10 random LHS samples of input variables x, y with associated Uniform distributions, respectively.

<?xml version="1.0" ?>
<Simulation>
  <RunInfo>
    <WorkingDir>LHS_mishra</WorkingDir>
    <batchSize>1</batchSize>
  </RunInfo>

  <GlobalSettings>
    <AnalysisType>LHS</AnalysisType>
    <limit>10</limit>
    <Inputs>x, y</Inputs>
    <Outputs>z</Outputs>
  </GlobalSettings>

  <Distributions>
    <Uniform name='x'>
      <lowerBound>-10</lowerBound>
      <upperBound>0</upperBound>
    </Uniform>
    <Uniform name='y'>
      <lowerBound>-6.5</lowerBound>
      <upperBound>0</upperBound>
    </Uniform>
  </Distributions>

  <Models>
    <ExternalModel ModuleToLoad="../../models/mishraBirdConstrained" name="mishra" subType="">
      <inputs>x, y</inputs>
      <outputs>z</outputs>
    </ExternalModel>
  </Models>

</Simulation>

When a dynamic model is provided, the users need to set <pivot> and <dynamic> node in the <GlobalSettings>. As illustrated in the following example.

<?xml version="1.0" ?>
<Simulation>
  <RunInfo>
    <WorkingDir>LHS</WorkingDir>
    <batchSize>1</batchSize>
  </RunInfo>

  <GlobalSettings>
    <AnalysisType>LHS</AnalysisType>
    <limit>10</limit>
    <Inputs>x0, y0, z0</Inputs>
    <pivot>time</pivot>
    <dynamic>True</dynamic>
    <Outputs>x,y,z</Outputs>
  </GlobalSettings>

  <Distributions>
    <Normal name="x0">
      <mean>4</mean>
      <sigma>1</sigma>
    </Normal>
    <Normal name="y0">
      <mean>4</mean>
      <sigma>1</sigma>
    </Normal>
    <Normal name="z0">
      <mean>4</mean>
      <sigma>1</sigma>
    </Normal>
  </Distributions>

  <Models>
    <ExternalModel ModuleToLoad="../models/lorentzAttractor.py" name="lorentzAttractor" subType="">
      <inputs>inputGroup</inputs>
      <outputs>outputGroup</outputs>
    </ExternalModel>
  </Models>

</Simulation>

In addition, the users can use inputGroup and outputGroup to represent input and output variable list. As illustrated in above example <ExternalModel> node.