EnrichedFEMUsingPINNs

Arxiv link : "Enriching continuous Lagrange finite element approximation spaces using neural networks"

This repo contains all the material needed to run the various numerical results obtained.

Documentation

A python documentation is available here.

Installation

The python code is based on the following 2 main modules:

• ScimBa (based on pytorch): for creation of the prior (PINNs prediction)
• FEniCS: for finite element resolutions (and eventually mshr for mesh generation)

We provide two ways of installing the necessary modules: the first via docker (https://docs.docker.com/engine/install/ubuntu/) and the second via anaconda (https://www.anaconda.com/docs/getting-started/anaconda/install).

Docker

A docker image is available via the command :

docker pull flecourtier/enrichedfem:1.0.0

Conda

• Create the conda environment and install FEniCS:

conda create -n enrichedfem -c conda-forge fenics mshr python=3.9.16
conda activate enrichedfem
conda update -n base -c defaults conda

• Install Pytorch:

conda install pytorch torchvision torchaudio pytorch-cuda=11.8 -c pytorch -c nvidia

• Install requirements and enrichedfem module (in editable mode): To be executed at the root of the git repo.

pip install -r requirements.txt
pip install -e .

• Install ScimBa (in editable mode):

git clone https://gitlab.inria.fr/sciml/scimba.git
cd scimba
pip install -e .