Graphon Control

Learning network interactions to steer collective behavior.

A PyTorch research implementation that learns how agents influence one another over time. It combines neural interaction kernels, differentiable simulation, and stochastic optimization.

Companion code for Optimal Graphon Control of Collective Dynamics, by Joseph K. Miller and Brandon Su.

Paper · Experiments · Figure reproduction

Experiments

• Opinion dynamics: Learn interactions that prevent fragmentation into isolated groups.
• Kuramoto oscillators: Learn interactions that untwist phase patterns and encourage alignment.

Both experiments compare learned control against baseline networks and save trajectories, diagnostics, plots, and animations.

Method

Encode agent labels → construct interaction weights → simulate dynamics → optimize with Adam.

The controller uses time and agent labels. Directed interaction weights are nonnegative and row-normalized. Simulations support deterministic dynamics and Brownian noise.

Quick start

From the repository root:

python3 -m venv .venv
source .venv/bin/activate
python -m pip install -e .
python e1_kuramoto.py --smoke --device cpu --no-mirror

This runs a 20-iteration workflow check on a small grid and network. Results appear under out_1/, including untwist.gif, kernel_time.gif, and metrics.json.

Reproduce the appendix

Regenerate the existing appendix figures and table statistics from the bundled original results, without training or simulation:

python reproduce_appendix.py --manifest appendix_manifest.json --output out/appendix-regenerated

See appendix reproduction for the archived runs, verification checks, and noise-data limitation.

Code

File	Contents
graphon_control/	Reusable controller, dynamics, objectives, and training
model_1.py	General experiment entry point
e1_kuramoto.py	Oscillator experiment
e2_bc.py	Opinion dynamics experiment
model_1_viz.py	Visualization utilities

Use python <script> --help for experiment options. See development for testing and reproduction, and numerical conventions for the connection to the paper.

Research scope

Controls are open loop and assume a known interaction law. Optimization searches a neural control family; global optimality is not certified. Receiver variation is measured rather than constrained during training.

MIT License