Data-driven model reduction of agent-based systems using the Koopman generator

This repository contains python codes for the article "Data-driven model reduction of agent-based systems using the Koopman generator" by Jan-Hendrik Niemann, Stefan Klus and Christof Schütte.

Niemann J-H, Klus S, Schütte C (2021) Data-driven model reduction of agent-based systems using the Koopman generator. PLoS ONE 16(5): e0250970. https://doi.org/10.1371/journal.pone.0250970

Agent-based models

There are three models predefined:

1. A voter model defined as a Markov jump process, VoterModel.py
2. An extended voter model defined on arbitrary networks, ExtendedVoterModel.py
3. A spatial predator-prey model, PredatorPreyModel.py

How to use?

1. Create measurements with demo_data_generation.py. The script illustrates the procedure using the agent-based model in VoterModel.py. There are some pre-generated measurements in the directory data/raw.
2. Process the data to obtain point-wise estimates of drift and diffusion. Use gEDMD to learn a global description. The procedure is demonstrated in demo_post_processing.py. There are some post-processed measurements in the directory data/processed. Further data-sets are available at
3. The reduced stochastic differential equation can now be simulated. This is demonstrated in demo_reduced_SDE.py.
4. The evaluation is demonstrated in demo_evaluation.py.

Additional Requirements

The codes require the d3s - data-driven dynamical systems toolbox: https://github.com/sklus/d3s