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. Nature Computational Science: https://www.nature.com/articles/s43588-024-00732-2

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.

Environment (HPC)

The upstream README assumes a personal laptop with python -m venv + pip install. On this HPC the recommended workflow is to use the system's pytorch module, which already provides torch + numpy + scipy + matplotlib for the right Python and CUDA. Only scikit-learn needs a one-time user install.

One-time setup (already done on this account):

module load pytorch/2.6.0-py3-cu11.8
pip install --user scikit-learn

This installs scikit-learn into ~/.local/lib/python3.13/site-packages, alongside the module's site-packages, and is picked up automatically whenever the module is loaded.

Every session — activate the stack with the loader:

source ~/load_dimon_env.sh

That single line:

• module purge
• module load pytorch/2.6.0-py3-cu11.8 (which itself pulls in python/3.13.3-gcc11, craype-accel-nvidia80, cuda/11.8.0)
• exposes torch (2.6.0+cu118), numpy, scipy, matplotlib
• exposes the user-installed scikit-learn

The loader is the analogue of ~/load_opencarp_env.sh (which activates the simulation stack). Use them in separate sessions, never together.

GPU note: torch.cuda.is_available() returns False on login nodes — that is expected. Submit GPU jobs to the gpu / gpu1 / gpu2 (production) or gdev (interactive dev) queues to actually train. Example interactive shell (replace walltime/resources for your queue's limits):

qsub -I -q gdev -l select=1:ncpus=8:ngpus=1:mem=64G -l walltime=01:00:00 -P personal-e1590340
# inside the interactive job:
source ~/load_dimon_env.sh
python -c "import torch; print(torch.cuda.is_available(), torch.cuda.get_device_name(0))"

Do not also activate BASE/dimon/. That venv is cray-python 3.9 and is reserved for PDF tooling (pypdf, pdfplumber); it has no torch and would mask the module's Python 3.13.

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.

1. Download data to the main folder (only required for Laplace/, ReactionDiffusion/, and the upstream LV/ example with public data — patient-specific cardiac data is not redistributable).

2. Activate the environment:

   source ~/load_dimon_env.sh

3. Run training from the example folder:

   cd Laplace        # or ReactionDiffusion / LV / DIMON_PINN / etc.
   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.

Project context

This fork lives at BASE/DIMON/ (where BASE = ~/cardiac_simulation/). It is the neural-operator side of the 12-lead ECG surrogate project — see BASE/CLAUDE.md for the full project overview, and BASE/literature/dimon_notes.md for our reading notes on the DIMON paper and how its example 3 maps onto our cohort.