khanmhmdi / pde-gcn

Official implementation code of the paper: "GCN-FFNN: A Two-Stream Deep Model for Learning Solution to Partial Differential Equations".

GCN-FFNN

Official implementation code of the paper: "GCN-FFNN: A Two-Stream Deep Model for Learning Solution to Partial Differential Equations" (Link).

Methodology

GCN Architecture

Results

The plots for 1D-Burgers equation for test nodes from outside the domain at t=0.5 and t=0.99:

The plots for 2D-Burgers equation for test nodes from outside the domain at t=3:

Usage

Install the required packages with pip install -r requirements.txt.

Navigate to the desired folder, e.g. pde-gcn/1d-burgers/ensemble-inner/.

For training run, e.g.:

python ensemble-inner.py

For testing run, e.g.:

python ensemble-inner.py --test

Citation

Please cite the paper using the following bibtex reference:

@article{BILGIN2022131,
title = {GCN-FFNN: A two-stream deep 
model for learning solution to partial 
differential equations},
journal = {Neurocomputing},
volume = {511},
pages = {131-141},
year = {2022},
issn = {0925-2312},
author = {Onur Bilgin and Thomas Vergutz 
and Siamak Mehrkanoon},
}