Reconstructing incomplete design-space data
Interlinear fills incomplete multivariate discrete data series by using information contained in nearby sampled gradients. Its principal method is the Distance-Weighted Gradient Network (DWGN).
Rather than fitting a single global response surface, DWGN reconstructs local curvature from neighbouring gradients. Known gradients are weighted according to distance and used to propagate information into unsampled parts of the discrete lattice.
Interface
use Sim::OPT::Interlinear;
Sim::OPT::Interlinear::interlinear(
"./sourcefile.csv",
"./confiinterlinear.pl",
"./obtainedmetamodel.csv"
);
The source CSV contains the discrete parameter levels in its coordinate columns and the objective in the final column. Missing objective values represent points to be reconstructed. Interlinear converts these coordinates to the same instance-name convention used by Sim::OPT.
Sampling structure
DWGN works naturally with structured or clustered samples such as star designs, central designs, block-coordinate samples and overlapping block-coordinate samples, because these provide neighbouring edges from which gradients can be obtained.
More uniformly distributed designs such as Latin hypercube or purely random samples can be less directly suited unless the sample is first expanded or the gradient neighbourhood is enlarged.
DWGN-simple and alternatives
The standard DWGN method is the active default. A simple modality provides a faster global form that is usually less accurate. Pure linear interpolation and nearest-neighbour reconstruction are also available as alternative modalities.
Computational controls
The cost of gradient reconstruction can increase with problem size. Configuration controls can limit the number of gradients and the distance over which gradients or points are considered.
References
Gian Luca Brunetti (2020), “Increasing the efficiency of simulation-based design explorations via metamodelling”, Journal of Building Performance Simulation, 13(1), 79–99. DOI: 10.1080/19401493.2019.1707875.
Gian Luca Brunetti (2020), “Grafting of design-space models onto models of different scope or resolution”, Journal of Building Performance Simulation, 13(3), 227–246. DOI: 10.1080/19401493.2020.1712477.