SS-PPCA: Stochastic Subspace via Probabilistic Principal Component Analysis

A methodology for efficient probabilistic characterization of model-form error via stochastic reduced-order modeling.

Model-form error is ubiquitous in computational science and engineering. Its probabilistic characterization is a critical and challenging problem.

SS-PPCA introduces probabilistic modeling of subspaces. The stochastic ROMs constructed using the stochastic subspaces are then used to characterize model error.

The code demonstrates the performance of SS-PPCA for characterization of model error.

Repository Contents

• Ex1/ — Parametric linear static problem.
• Ex2/ — Linear static problem for characterizing high-dimensional model (HDM) error.

Requirements

• MATLAB R2023b or later (older versions might also work, but are not tested).
• Required Toolboxes:
  • Statistics and Machine Learning Toolbox
  • Optimization Toolbox

Running the Experiments

1. Clone the repository:

   git clone https://github.com/UQUH/SS_PPCA.git
   cd SS_PPCA

2. Open MATLAB and set the repository folder as the working directory.

3. Run the scripts for different examples.

4. Results and figures will be saved automatically in the results/ folder.

Each example (Ex1, Ex2) contains a separate model folder and method folder SS-PPCA:

• SS-PPCA: Stochastic Subspace via Probabilistic Principal Component Analysis.

Citation

If you found SS-PPCA helpful, please cite the following paper:

@Article{yadav2025ss,
  author  = {Akash Yadav and Ruda Zhang},
  journal = {Computational Mechanics},
  title   = {Stochastic Subspace via Probabilistic Principal Component Analysis for Characterizing Model Error},
  year    = {2025},
  doi     = {10.1007/s00466-025-02701-6},
}

The Team

The SS-PPCA method is developed by the Uncertainty Quantification Lab at the University of Houston.

The primary contributors are:

• Akash Yadav
• Ruda Zhang