README.md

Kernel Expansions for Mean-Field Control

Pytorch implementation of our approach for solving high-dimensional mean-field control problems with nonlocal interactions

Associated Publications

Kernel Expansions for High-Dimensional Mean-Field Control with Nonlocal Interactions

Please cite as

@misc{vidal2024kernel,
      title={Kernel Expansions for High-Dimensional Mean-Field Control with Non-local Interactions}, 
      author={Alexander Vidal and Samy Wu Fung and Stanley Osher and Luis Tenorio and Levon Nurbekyan},
      year={2024},
      eprint={2405.10922},
      archivePrefix={arXiv},
      primaryClass={math.OC}
}

Set-up

Install all the requirements:

pip install -r requirements.txt 

Double Integrator Obstacle Experiments

Train and plot trajectories for interacting agents using double integrator dynamics that fly around two rectangular objects and reach a target on the other side.

driver_train_doubleintegrator.ipynb

Quadcopter/Quadrotor Experiments

Train and plot trajectories for interacting agents using quadrotor dynamics for up to 5000 agents.

driver_train_quadrotor.ipynb

Train convergence timing experiment.

driver_train_quadrotor_convergence.py

Plot saved convergence timing experiment.

driver_plot_quadrotor_convergence_comparison.ipynb

Generate and plot trajectories using previously trained a_coeff.

driver_pretrained_acoeff_primal.ipynb

Generate Kernel Approximation Network

Train, plot, and save network parameters for basis functions used to approximate the kernels in other experiments.

train_kernelbasis_nn.ipynb