🌀 Interfere

A Python package for modeling and predicting the response of complex dynamic systems to interventions.

Overview

Interfere is a research-oriented Python package that addresses a fundamental question in complex systems: When can we predict how complex systems will respond to interventions? This package provides tools for:

• Modeling dynamic nonlinear multivariate stochastic systems.
• Simulating and analyzing how such systems respond to interventions.
• Generating complex dynamic counterfactuals.
• Studying causal relationships in complex systems.

Interfere Benchmark Dataset (Download)

The image above depicts the uninterrupted trajectories of sixty dynamic models in blue and their response to a particular intervention in red. This data is available for download as the Interfere Benchmark 1.1.1. It can be used to benchmark a forecasting method's ability to predict the response of a dynamic system to interventions.

Installation

From pip

pip install interfere

From Local Clone

git clone https://github.com/djpasseyjr/interfere.git
cd interfere
pip install .

Quick Start

The Interfere package is designed around three main tasks: counterfactual simulation, predictive method optimization, and prediction. Here's a complete example using the SINDy (Sparse Identification of Nonlinear Dynamics) method:

1. Counterfactual Simulation

First, let's create and simulate a dynamic model:

import numpy as np
import interfere
import optuna

# Set up simulation parameters
initial_cond = np.random.rand(3)
t_train = np.arange(0, 10, 0.05)
dynamics = interfere.dynamics.Belozyorov3DQuad(sigma=0.5)

# Generate trajectory
sim_states = dynamics.simulate(t_train, initial_cond)

2. Applying an Intervention

Next, we'll apply an intervention to one component of the system:

# Time points for the intervention simulation
test_t = np.arange(t_train[-1], 15, 0.05)

# Intervention initialization
intervention = interfere.SignalIntervention(iv_idxs=1, signals=np.sin)

# Simulate intervention
interv_states = dynamics.simulate(
    test_t,
    prior_states=sim_states,
    intervention=intervention,
)

3. Model Optimization and Prediction

Using the generated data, we can run hyperparameter optimization with a forecasting method. All forecasting methods come with reasonable hyperparameter ranges built in.

# Select the SINDy method for hyperparameter optimization.
method_type = interfere.SINDy

# Create an objective function that aims to minimize cross validation error
# over different hyper parameter configurations for SINDy
cv_obj = interfere.CrossValObjective(
    method_type=method_type,
    data=sim_states,
    times=t_train,
    train_window_percent=0.3,
    num_folds=5,
    exog_idxs=intervention.iv_idxs,
)

# Run the study using optuna.
study = optuna.create_study()
study.optimize(cv_obj, n_trials=25)

# Collect the best hyperparameters into a dictionary.
best_param_dict = study.best_params

4. Intervention Response Prediction

Using the best parameters found, we can fit the forecasting method to pre-intervention data and then make a prediction about how the system will respond to the intervention.

# Initialize SINDy with the best perfoming parameters.
method = interfere.SINDy(**study.best_params)

# Use an intervention helper function to split the pre-intervention data
# into endogenous and exogenous columns.
Y_endog, Y_exog = intervention.split_exog(sim_states)

# Fit SINDy to the pre-intervention data.
method.fit(t_train, Y_endog, Y_exog)

# Use the inherited interfere.ForecastingMethod.simulate() method
# To simulate intervention response using SINDy
pred_traj = method.simulate(
    test_t, prior_states=sim_states, intervention=intervention
)

The SINDy method identifies the underlying dynamics of the system using sparse regression techniques, making it particularly effective for discovering interpretable mathematical models of complex systems.

Dependencies

Core dependencies:

• matplotlib
• networkx
• numpy
• optuna
• pyclustering
• pysindy
• scikit-learn
• statsmodels
• typing_extensions

Optional dependencies for additional methods:

• neuralforecast
• statsforecast
• sktime

Example

The package can be used to simulate and analyze how systems respond to interventions. For example, it can model the effect of stochasticity on intervention response forecasting:

Documentation

For a more detailed explanation of the purpose of the package refer to paper.pdf.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Citation

If you use this software in your research, please cite:

@article{passey2024interfere,
  title={Interfere: Intervention Response Simulation and Prediction for Stochastic Nonlinear Dynamics},
  author={Passey, D. J. and Mucha, Peter J.},
  journal={arXiv preprint},
  year={2025}
}

Contact

• Author: DJ Passey (djpassey@unc.edu)
• Institution: University of North Carolina at Chapel Hill