Sample generation

In order to run sample generation, we set the option main/mode to be sample_generation in the input file. In the example of examples/poisson/poisson.sample.yml,

main:
  mode: sample_generation
  use_rom: true
  solver: poisson

There are two types of sampling:

• base sample generator that samples over uniform grid points on parameter space
• random sample generator that randomly choose the parameter values over a uniform random distribution

Base sample generator

In the example of examples/poisson/poisson.sample.yml, we use base sample generator, saving snapshots in the name of poisson0,

sample_generation:
  type: base
  file_path:
    prefix: "poisson0"

Specifying the list of sampling parameters

The list of parameters to be sampled is specified in the input file under sample_generation/parameter. In the example of examples/poisson/poisson.sample.yml, we sample over one parameter:

sample_generation:
  parameters:
    - key: single_run/poisson0/k
      type: double
      sample_size: 3
      minimum: 2.0
      maximum: 3.0

For each parameter listed, base sample generator creates an 1D uniform grid space between minimum and maximum with the specified sample_size. In sample generation, base sample generator replaces the value of the input option key with a sample value, and executes a single-run. Running the main driver with this input file

cd examples/poisson/
../../bin/main -i poisson.sample.yml

executes three single-runs that solve for Poisson equation with a sample value for parameter single_run/poisson0/k.

Technically, any option within the input file can be chosen as a sampling parameter. Currently, however, we only support double and filename type of input options. The example examples/poisson/poisson.sample.2d.yml samples over global configuration files for component meshes as an additional parameter:

sample_generation:
  parameters:
    - key: single_run/poisson0/k
      type: double
      sample_size: 3
      minimum: 2.0
      maximum: 3.0
    - key: mesh/component-wise/global_config
      type: filename
      sample_size: 4
      minimum: 1
      maximum: 4
      format: "config/sample.config-%02d.h5"

For filename parameter, the key input option is set to a string that follows the format with an integer index. The integer index is chosen from 1D uniform grid space of size sample_size between minimum and maximum In this example, 4 global configuration files will be used for sampling:

• config/sample.config-01.h5
• config/sample.config-02.h5
• config/sample.config-03.h5
• config/sample.config-04.h5

If multiple $N$ sampling parameters are listed, then base sample generator creates an $N$-D uniform grid space accordingly. For the $i$-th sampling parameter with sample size $S_i$, we have the total sample size of $$S = \prod_{i=1}^N S_i.$$

Running the example input file above

../../bin/main -i poisson.sample.2d.yml

will collect $3\times4=12$ samples with different single_run/poisson0/k values and mesh/component-wise/global_config files.

Random sampling