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PME-toolkit

PME-toolkit is a framework for design-space dimensionality reduction in parametric shape optimization, based on:

  • Parametric Model Embedding (PME)
  • Physics-Informed PME (PI-PME)
  • Physics-Driven PME (PD-PME)

The toolkit provides a reproducible, data-driven workflow to construct low-dimensional representations of high-dimensional parametric design spaces while preserving a direct link to the original variables.

Python for daily use. MATLAB for reference validation.

Project status

PME-toolkit is a released research software package (v1.2):

The Python implementation is fully functional and recommended for use.
MATLAB remains available as a reference implementation for validation and comparison.

What the toolkit does

PME-toolkit enables:

  • reduction of high-dimensional parametric design spaces
  • extraction of dominant modes of variability
  • construction of interpretable latent representations
  • reconstruction of original variables through backmapping
  • reproducible benchmarking across methods and datasets

Minimal workflow

A typical PME workflow consists of:

  1. preparing input data (geometry, variables, optional physics)
  2. defining a JSON configuration file
  3. running the dimensionality reduction
  4. analyzing results and visualizations
  5. optionally performing backmapping

Reproducibility and benchmarks

PME-toolkit is designed for reproducible benchmarking across methods and datasets.

Validated on:

  • a tiny self-contained glider case (included in the repository)
  • benchmark configurations for airfoil and underwater glider geometries
  • larger datasets available via Zenodo

All workflows are defined through JSON configuration files, ensuring full reproducibility of experiments.

Why PME-toolkit?

PME-toolkit extends classical PCA-based approaches through a generalized, weighted formulation tailored to parametric design problems.

  • Analytical backmapping (core feature)
    Reduced coordinates can be mapped back exactly to the original parametric variables.

  • Generalized formulation with weights
    PME relies on a weighted POD/PCA formulation, where weights can encode the role of variables (including null weights).
    This formulation is not equivalent to standard PCA and cannot be reduced to a simple SVD.

  • Design-aware latent space
    Unlike standard PCA (typically applied to state snapshots without variables), PME explicitly incorporates parametric design variables into the embedding.

  • Physics-aware variants
    PI-PME and PD-PME embed physical information into the dimensionality-reduction process.

Result: interpretable and optimization-ready reduced spaces.

Key concepts

  • Embedding → projection of the design space into a reduced latent space
  • Modes → principal directions of variability
  • Retained variance → fraction of variance captured by the reduced space
  • Backmapping → reconstruction of original variables from reduced coordinates

Documentation structure

  • Quickstart → run the tool immediately
  • Workflow → full pipeline description
  • Input data → required data structure
  • Configuration → JSON specification
  • Benchmarks → predefined test cases
  • Datasets → dataset organization
  • Backmapping → reconstruction process
  • Visualization → interpretation of results
  • APIs → Python and MATLAB interfaces
  • Reproducibility → validation workflows

Philosophy

PME-toolkit is designed to support:

  • reproducible research
  • transparent dimensionality reduction workflows
  • systematic comparison between methods
  • integration with optimization pipelines

The toolkit follows a configuration-driven approach, where experiments are fully defined through JSON files and can be reproduced across environments.

Citation

If you use PME-toolkit in your work, please cite the associated publication (see the Citation page).