Variables

[Rykath]

Gathering a few ideas and observations related to Variables

Requirements

• the target simulation takes several parameters and returns several output variables
• the parameters follow a specified distribution
• for Active Learning and flexible number of points, the samples need to be drawn iteratively
• Variables and Encoders are connected: e.g. LogUniform usually requires a LogEncoder for a good fit
• Some inputs/outputs are vector/matrix/tensor valued
• Some inputs/outputs are functions in theory, vectors over support points or a combination of basis functions in practice
  • for fitting and analysis, a dimensionality reduction is vital

Current Status

• Input, Independent & Output
  • Input: Constant, Linear, Uniform, LogUniform, Normal, Halton, Active Learning
• only linearly spaced independent variables
• designed for continuous values only

Ideas for Improvement

• separate the specification of the sampling distribution from the sampling method
  • Distribution/Transformation/Encoder: Linear / Uniform, Logarithmic / LogUniform, Gaussian → Encoders #160
  • Method: Grid, Random (uniform), Halton (quasi-random), Constant/Fixed (could be multiple)
  • Advantage: Sampling method can be changed easily, Encoder mostly depends on the spacing, adding new distributions or methods can be done independently
  • Connection: Each sampling method assumes a linear spacing, a transformation / encoder is used to map it to the specified distribution
• four types of variables
  • Input - relevant dimensions for sampling and active learning
  • Output
  • Constant - ignored in Surrogate but usable in the Worker, possibly allow a list of constants and each step shall be run for each set of constants in parallel?
  • Independent - fixed values, expanded to axis or reduced to index in Surrogate
• Active Learning is a separate section, and not a method
  • uses the sampling method for the warmup phase
  • searches and proposes new samples for the specified variables, takes the sampling method for all others
• load user specified parameters and old data
• discrete variables
• function valued variables
  • high dimensionality
    • high number of support points
    • support points follow a spacing / distribution themselves, usually continuous
  • best practice: decomposition / dimensionality reduction
  • alternative for function outputs: surrogate treats the independent dimension just as another input dimension
  • for inputs: how to specify constraints, how to sample
  • idea (by Maximilian): specify import(profiles.nc) to load example profiles, then run a PCA and sample from the components
• tensor valued variables
  • low dimensionality - indices, discrete
  • can be uncorrelated
  • sometimes dimensionality reduction is possible
  • shouldn’t need an additional index variable - only specify shape
• some variables are connected differently
  • most prominent: mean & error
  • Use case: heteroscedastic noise
  • should this relation be specified? If so, how?

Proposed example configuration

variables:
  u: Uniform(min, max)  # ~ Linear
  v: Logarithmic(min, max, base=10)  # ~ Log, LogUniform
  x: Gaussian(mean, std)  # ~ Normal
  y: - Logarithmic
     - Gaussian(mean, std)  # ~ LogGaussian
  f: - import(profile.nc) 
     - PCA(n or tol)
sampling:
  n: 10
  Random: u, v  # ~ Uniform
  Halton: x, y
  Grid:  f
activelearning:
  n: 30
  variables: x, y, f  # u, v sampled randomly

[Rykath]

The (proposed) Data Flow: