GP-BayesOpInf

This repository contains the source code for the numerical experiments in the paper

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

by
Shane A. McQuarrie (Sandia National Laboratories),
Anirban Chaudhuri (The University of Texas at Austin),
Karen E. Willcox (The University of Texas at Austin), and
Mengwu Guo (Lund University).

BibTex

@misc{mcquarrie2024gpbayesopinf,
    title = {Bayesian learning with {G}aussian processes for low-dimensional representations of time-dependent nonlinear systems},
    author = {Shane A. McQuarrie and Anirban Chaudhuri and Karen E. Willcox and Mengwu Guo},
    year = {2024},
    eprint = {2408.03455},
    archivePrefix = {arXiv},
}

Contents

• codebase/: implementation of the main elements of GP-BayesOpInf.
• models/: full-order models used to generate data for the numerical experiments.
• PDEs/: implementation of GP-BayesOpInf for PDE problems with a single trajectory of training data.
• PDEsMulti/: implementation of GP-BayesOpInf for PDE problems with multiple trajectories of training data.
• ODEs/: implementation of GP-based Bayesian parameter estimation for ODE problems.

Installation

This repository uses the standard Python scientific stack (NumPy, SciPy, Scikit-Learn, etc.) and the opinf package. We recommend installing the required packages in a new conda environment.

$ conda deactivate
$ conda create -n gpbayesopinf python=3.12
$ conda activate gpbayesopinf
(gpbayesopinf) $ pip install -r requirements.txt

Reproducing Numerical Results

Each of the three numerical experiments detailed in the paper is contained in its own folder.

• Compressible Euler equations: PDEs/
• Nonlinear diffusion-reaction equation: PDEsMulti/
• SEIRD epidemiological model: ODEs/

To reproduce the figures in the paper, navigate to the directory and run experiments.sh.

cd PDEs/
./experiments.sh