Learning high-dimensional McKean-Vlasov forward-backward stochastic differential equations with general distribution dependence

Jiequn Han, Ruimeng Hu, Jihao Long

Link to code repository: https://github.com/frankhan91/DeepMVBSDE

Dependencies

• Quick installation of conda environment for Python: conda env create -f environment.yml

Running

Quick start for 2d version of the benchmark example with explicit solution in Section 4.1 of paper:

python main.py

You should be able to observe the program beginning its training within one minute. The total runtime is approximately 800 seconds on a MacBook Pro equipped with a 2.40 GHz Intel Core i9 processor. The configuration employs small parameters and short iterations, intended solely for testing purposes.

To run experiments related to Figure 1 in paper

python main.py --config_path configs/sinebm_d10.json

The experiments for d=5 can be conducted by setting dim to 5 in eqn_config. To employ the DBDP method for solving BSDEs, modify the loss_type field in net_config, changing it from DeepBSDE to DBDPiter.

To run experiments related to Figure 2 in paper, for d=15

python main.py --config_path configs/sinebm_d15.json

To run solvers with other dimensions: d=5, 8, 10, 12, change N_simu and N_simu to 500, 800, 1000, 1200, respectively, and change num_hiddens in both eqn_config and net_config to [12, 12], [18, 18], [24, 24], [30, 30], respectively.

To solve MFG of Cucker-Smale flocking model in Section 4.2 of paper

python main.py --config_path configs/flock_d3.json

Citation

Han, Jiequn, Ruimeng Hu, and Jihao Long. Learning high-dimensional McKean-Vlasov forward-backward stochastic differential equations with general distribution dependence. arXiv preprint arXiv:2204.11924, accepted to SIAM Journal on Numerical Analysis (2022)

If you find this work helpful, please consider starring this repo and citing our paper using the following Bibtex.

@article{HanHuLong2022deepmvbsde,
  title={Learning high-dimensional McKean-Vlasov forward-backward stochastic differential equations with general distribution dependence},
  author={Han, Jiequn and Hu, Ruimeng and Long, Jihao},
  journal={arXiv preprint arXiv:2204.11924, accepted to SIAM Journal on Numerical Analysis},
  year={2022}
}

Contact

Please contact us at jiequnhan@gmail.com if you have any questions.