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Bayesian Calibration and Uncertainty Quantification for Fractional-Order Constitutive Models

Welcome to the documentation for the Bayesian Inference and Uncertainty Quantification of Fractional-Order Constitutive Models framework. This repository provides computational tools to apply machine learning and Bayesian inference techniques to complex mechanical models.

Overview

Fractional-order constitutive models are powerful tools for capturing the memory-dependent and anomalous behavior of materials, especially thoese with power-law behavior spanned across decades of time scales. In this study and repository, Bayesian calibration with MCMC sampling technique (NUTS algorithm in PyMC package) are utilized to infere the model parameters, construct their posterior distributions, and quantify the uncertainties in the model responses.

Repository Structure

  • configs/: Configuration files for setting up MCMC chains, priors, and model hyperparameters.
  • datasets/: Synthetic experimental dataset and optimized model parameters used for the calibration process.
  • notebooks/: Jupyter notebook equivalents of the python codes for interactive use.
  • scripts/: Main inference script, helper functions, and post-processing scripts.
  • results/: Output directories for trace plots, posterior distributions, predictive checks, etc.

Installation

First, clone the repository and navigate into the project directory:

git clone git@github.com:armankhoshnevis/BI-and-UQ-of-Fractional-Order-Constitutive-Models.git
cd BI-and-UQ-of-Fractional-Order-Constitutive-Models

If it is preferred to use standard Python virtual environments locally, pip alongside the requirements.txt file can be used. Then, execute the following commands:

python -m venv env

# On Windows:
.\env\Scripts\activate

# On macOS/Linux:
source env/bin/activate

pip install -r requirements.txt

If it is preferred to run the codes on a cluster, environment.yml file is used to ensure exact dependency and Python version matching. Then, execute the following commands:

module load Miniforge3 # Replace with your specific cluster's module if different
conda env create -f environment.yml
conda activate UQ_Project

Quick Run

Running Locally

Once your environment is activated (via Conda or venv), navigate to the script directory and execute the Python files directly from your terminal:

cd script
python MCMC_FMG_Inference.py --HS 20
python MCMC_FMG_Inference_PostProcessing.py --HS 20

Running on a SLURM Cluster

If you are running the inference on a cluster that uses the SLURM workload manager, a sample batch script (MCMC_FMG.sh and MCMC_FMM.sh) is provided. The script is pre-configured to activate the UQ_Project conda environment.

cd script
sbatch MCMC_FMG.sb

Note: The script's output and any errors will be automatically logged to standard .out and .err files in the working directory.

Citation Requirements

If you use this software, please cite it and its corresponding paper, as:

  • Software citation:

  • APA style: Khoshnevis, A. (2026). Bayesian Calibration and Uncertainty Quantification for Fractional-Order Constitutive Models (Version 1.0.0) [Computer software]. https://github.com/armankhoshnevis/BI-and-UQ-of-Fractional-Order-Constitutive-Models

  • BibTeX entry:
    @software{Khoshnevis_Bayesian_Calibration_and_2026,
    author = {Khoshnevis, Arman},
    license = {Apache-2.0},
    month = mar,
    title = {{Bayesian Calibration and Uncertainty Quantification for Fractional-Order Constitutive Models}},
    url = {https://github.com/armankhoshnevis/BI-and-UQ-of-Fractional-Order-Constitutive-Models},
    version = {1.0.0},
    year = {2026}
    }

  • Paper citation: Will be provided once published.

Contributions

This repository is a static archive of the project code. The software is provided "as-is" and is not actively maintained. Please see CONTRIBUTING.md for more details.