Mapping Uncertainty Using Differentiable Programming

Welcome to the repository supporting the paper "Mapping Uncertainty Using Differentiable Programming." This repository contains all the necessary code and data to reproduce the case studies and results presented in the manuscript.

📂 Repository Contents

Below is an overview of the files included in this repository:

🔹 Models & Simulations

• DMA_MR_ss.py – Python script for the steady-state model (ODE system) of the Membrane Reactor System (DMA-MR).
• cstr_example.ipynb – Jupyter Notebook demonstrating a Continuous Stirred Tank Reactor (CSTR) example/case study.
• dma_mr_example_forward.ipynb – Jupyter Notebook showcasing the forward uncertainty propagation case study for the DMA-MR system.
• dma_mr_inverse_uncertainty_mapping.py – Python script implementing the inverse uncertainty propagation for the DMA-MR case study.
• cstr_example_bimodal.ipynb – Jupyter Notebook demonstrating a variation of the CSTR case-study where the uncertainty region is described by a bimodal distribution (mixture of Gaussians), to illustrate that the proposed approach works well for complex distributions.
• proof-of-concept-3d-continuation.ipynb – Jupyter Notebook showing a proof-of-concept of a high-dimensional (3D) mapping of an uncertainty region defined by an ellipsoid.
• fed-batch-reactor-3d-continuation.ipynb – Jupyter Notebook showing a 3D uncertainty inverse mapping of state variables of a fed-batch biological reactor. The main complication, besides the higher dimensionality, is the fact that the system equations need to be numerically integrated as an analytical solution does not exist, similar to the DMA-MR case-study.

📊 Data & Visualization

• montecarlo.npz – NumPy data file containing results from 10,000 Monte Carlo simulations, used for comparison with the proposed approach.
• generate_plots_dma_mr.py – Python script for generating all figures for the DMA-MR inverse uncertainty propagation case study using the Monte Carlo data.
• time_montecarlo_dma_mr.png – Screenshot of the computational time required to run all 10,000 MC simulations, executed on a Lenovo Laptop (32GB RAM, Ryzen 7 5800H, Windows 11).

🔧 Getting Started

To run the models and generate results, ensure you have the required Python dependencies installed. You can set up the conda environment using:

conda create --name <env> --file requirements.txt

📜 Usage

• Open Jupyter notebooks (.ipynb files) to explore forward and inverse uncertainty propagation.
• Run or import the functions from the Python scripts (.py files) to simulate models and generate plots.

📖 Citation

If you use this code in your research, please cite our paper:

"Mapping Uncertainty Using Differentiable Programming"

(Full citation details will be added here once available)

🤝 Contributing

Feel free to open issues or submit pull requests if you find any bugs or improvements!

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📌 Maintainer: Victor Alves
📧 Contact: GitHub