Gaussian Process for Learning PDEs with Uncertain Data Locations

This repository provides the implementation and experimental results for the paper:

PDE-Constrained Gaussian Process Surrogate Modeling with Uncertain Data Locations
Dongwei Ye, Weihao Yan, Christoph Brune, Mengwu Guo

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Overview

Gaussian Process (GP) regression is a state-of-the-art method for data-driven modeling and function approximation. This repository implements a Bayesian approach to GP regression that accounts for uncertainties in input data locations, addressing common challenges in learning partial differential equations (PDEs) from noisy and uncertain data.

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Installation

1. Install required dependencies:

   pip install -r requirements.txt
   

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Usage

Run the script with the appropriate function key to reproduce the results:

python run.py <function_key>

Available Function Keys

• h: Run experiments on the heat equation.
• rd: Run experiments on the reaction-diffusion equation.
• loadForPred: Load heat inference data for predictive analysis.
• loadForPred_rd: Load reaction-diffusion inference data for predictive analysis.

Examples for PDEs

Run the heat equation experiment:

python run.py h

Load reaction-diffusion data for predictive analysis:

python run.py loadForPred_rd

Examples for 1D functions

All the codes related to the 1D-function examples are located in the folder 1Dfunction. Enter the directory and run the experiments with:

python run.py

Different 1D functions can be chosen for the test. The complete list of available functions is demonstrated in 1Dfunction/include/func.py