Mean Field Tools

A Python library for numerically solving McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs) under common noise using elicitability, deep learning and Picard iterations.

It accompanies the paper Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise — see How to cite this work.

Features

• Deep BSDE (Backward Stochastic Differential Equation) solvers
• Forward-Backward SDE implementations with Picard iteration
• Neural-network function approximators (including ResNet architectures)
• Mean field flow measure approximations (with common-noise support)
• Filtration tools for Brownian motion and stochastic state tracking

Installation

# Clone the repository
git clone https://github.com/fjpAntunes/mean-field-tools.git
cd mean-field-tools

# Install with Poetry
poetry install

Usage

See mean_field_tools/deep_bsde/README.md for a detailed overview of the components, and mean_field_tools/deep_bsde/script/experiments/ for runnable examples (systemic risk, portfolio hedging, economic growth, and more).

Testing

The project uses pytest for testing. Tests are organized into unit and integration tests within the mean_field_tools/deep_bsde/test/ directory.

# Run all tests
pytest

# Run specific test categories
pytest mean_field_tools/deep_bsde/test/unit/
pytest mean_field_tools/deep_bsde/test/integration/

# Run a specific test file
pytest mean_field_tools/deep_bsde/test/unit/test_function_approximator.py

Structure

• mean_field_tools/deep_bsde/: Core library — the Deep BSDE solver and its components
  • filtration.py: Brownian motion generation and stochastic state tracking
  • forward_backward_sde.py: Forward/Backward SDE classes and Picard iteration
  • function_approximator.py: Neural-network approximators
  • measure_flow.py: Mean field flow measure approximations
  • artist.py: Plotting and diagnostics
  • script/experiments/: Example applications
  • test/: Unit and integration tests

How to cite this work

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

Felipe J. P. Antunes, Yuri F. Saporito, and Sebastian Jaimungal. Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise, 2026. arXiv:2512.14967.

@misc{antunes2026deeplearningelicitabilitymckeanvlasov,
      title={Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise},
      author={Felipe J. P. Antunes and Yuri F. Saporito and Sebastian Jaimungal},
      year={2026},
      eprint={2512.14967},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2512.14967},
}

License

MIT