SS-Bootstrap: Stochastic Subspace via Bootstrap

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-Bootstrap 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-Bootstrap in characterizing model error.

Repository Contents

• Ex1/ — Parametric linear static problem.

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_Bootstrap.git
   cd SS_Bootstrap

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

3. Run the scripts.

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

Example (Ex1) contains a separate model folder and method folder SS_PPCA, SS_Bootstrap:

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

Citation

If you found SS-PPCA/SS-Bootstrap 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 and SS-Bootstrap methods were developed by the Uncertainty Quantification Lab at the University of Houston.

The primary contributors are:

• Akash Yadav
• Ruda Zhang