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Backmapping

Backmapping reconstructs original design variables from reduced coordinates using a previously computed PME model.

Overview

Backmapping maps a point in the reduced space:

x ∈ R^N

to an approximation of the original design variables:

u ≈ u_hat

This enables:

  • interpretation of latent variables
  • reconstruction of physical configurations
  • integration with optimization workflows

Requirements

Backmapping requires:

  • a trained embedding model (from a previous PME run)
  • a reduced coordinates vector
  • the original configuration file used to build the model

Execution

Python

pme-back case_back.json

MATLAB

run_back("case_back.json")

Configuration

Backmapping is defined through a dedicated JSON file.

See:

  • Backmapping configuration

for the complete specification.

Input

The reduced coordinates are provided through an external file (e.g. .txt):

  • each configuration corresponds to one vector x
  • dimensionality must match the number of retained modes

Output

Backmapping produces:

  • reconstructed design variables
  • optionally formatted outputs for downstream use

Output format and layout are defined in the configuration file.

Denormalization

Backmapping includes a denormalization step that maps reduced coordinates back to the original variable scale.

This depends on:

  • dataset statistics
  • selected denormalization rule (e.g. "3sigma")

Notes

  • dimensionality of x must match the retained modes
  • values should lie within the training domain
  • extrapolation may produce non-physical or invalid configurations
  • results depend on the quality of the original embedding

Summary

Backmapping is a post-processing step that closes the PME workflow by linking reduced representations back to interpretable design variables.