gninvert

The purpose of this project is to explore (and develop tools for) the process of "inverting" graph networks (GNs): rather than using a GN to simulate or make predictions, the goal is to find a GN with interpretable symbolic message and update functions that might have generated a given data set.

This is done in two ways:

• First, train a graph neural network (GNN), i.e. make its message and update functions neural networks and train them to approximate the behaviour of certain time series data
• Second, take the GNN, and use symbolic regression to fit equations to what it has learned. This gives a GN with interpretable functions, rather than a black-box GNN.

The method is based on this paper.

In addition to the inversion, the project contains code for several GN-based simulations, which generate the data. These simulations are inspired by simplified versions of the cell morphogenesis models in this paper. Cell morphogenesis models are the main application area considered in this project.

Setup & Dependencies

First, you need to install the programming language Julia, required by PySR (which is a Python library, like all of gninvert, but internally uses Julia).

Second, you must use Pyenv as your Python environment manager because otherwise PySR will throw a fit and probably need to reinstall itself on every run. Specifically, you need to create a Pyenv environment by doing something like this: PYTHON_CONFIGURE_OPTS="--enable-shared" pyenv install 3.9.10.

After these steps, and making sure that Pyenv is working (which pip and which python should both show non-default values, specifically paths that include words like .pyenv and/or shims in them), you can simple run chmod +x dependecy_install.sh and ./dependency_install.sh in succession in a terminal in the root gninvert folder and this will install the Python packages for you (and configure PySR).

The packages installed are:

• PyTorch
• PyTorch Geometric
• gplearn
• NumPy
• Pandas
• Jupyter Lab (only required for notebook-related stuff)
• ipywidgets (only required for notebook-related stuff)
• tqdm (only required for notebook-related stuff)
• matplotlib
• networkx
• einops
• PySR

Example usage

The following command, run in the project directory, will do a hyperparameter search using the "general" hyperparameter settings over data from the 'diff2' model (diffusion network with two chemicals), running each hyperparameter setting 5 times, and saving the results:

python run.py -m diff2 -p general -r 5 -n name_to_save_under

The file run.py lists available models and hyperparameter options, in a format that is easy to extend yourself.

Other options available:

• pass -s 1 to skip the symbolic regression and only do the hyperparameter search
• pass -S 1 to only do symbolic regression (on the model specified using -m directly, rather than on data generated from that model), skipping the hyperparameter search and the GNN training
• pass -c simulation or -c loss to change whether the best GNN model is selected based on how accurately it simulates the original GN model, or on last-step validation loss in the training loop.