DIffeomorphic-Mapping Operator learNing (DIMON)

We introduce a neural operator framework, named DIffeomorphic Mapping Operator learNing (DIMON), which allows AI to learn geometry-dependent solution operators of different types of PDEs on a wide variety of geometries. Arxiv: https://arxiv.org/abs/2402.07250

Data: https://doi.org/10.5281/zenodo.13958884

Note: Data in example 3 is not included in this link as the heart geometries are patient-specific clinical data. Data in Example 3 can be provided by request to the corresponding authors and potentially after an IRB for sharing data is approved.

Environments

python >= 3.7.4

torch >= 1.2.0 (this legacy version is compatible with CUDA==10.2, the new versiosn can be used if CUDA driver is compatible.)

pip >= 24.0

Installation requires about 1 min on a personal laptop. torch version has to be compatible with the CUDA driver. https://pytorch.org/get-started/previous-versions/

Examples

This repository contains three examples: solving the Laplace equation on 2D domains, solving reaction-diffusion equations on 2D annulus, and predicting electrical wave propagation on patient-specific left ventricles.

0. download data to the main folder

1. create a virtual environment and install packages

python -m venv dimon

source YOUR_PATH/dimon/bin/activate

pip install torch matplotlib scipy scikit-learn

2. network training

cd EXAMPLE_FOLDER

python main.py --epoch 10000

Note: please train with the same number of epochs to reproduce the results in the paper.

Note: the ten Tusscher model is adopted from the cellular model in CellML repository.