The official repository for the results and the source code used in the work:
Huang, Han, and Rongjie Lai. "Unsupervised solution operator learning for mean-field games." Journal of Computational Physics (2025): 114057. [arXiv]
During inference, our method maps a MFG problem setup to its solution via a single forward pass computed in under 1 second. In constrast, traditional optimization methods take minutes while deep learning methods require hours due to the need for re-training.
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We showcase trained models' consistent behavior on input samples of varying sizes; this demonstrates we are indeed parametrizing the MFG solution operator, a mapping between infinite dimensional spaces.
| 1024 samples | 2048 samples | 4096 samples |
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| 2106 samples | 3510 samples | 7020 samples |
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Conceptually, this example models a group of agents wishing to travel from a location at the top to one at the bottom. Meanwhile, they want to avoid the two obstacles in the middle and minimize the distances traveled.
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Tested with Python 3.9 and PyTorch 1.13.
One can run the expriments shown in the paper by calling python main_corr.py with different arguments. Each run creates a directory at ./results/<dataset name>/<experiment name> to store all the relevant information for plotting, etc.
The experiments are moderately memory intensive - interaction-free MFG uses around 6 to 10GB of VRAM, while MFG with interaction terms may require ~20GB. Try reducing the batch size or number of samples per distribution if you get OOM errors.
To run the experiment, do:
python main_corr.py --N_iter 50000 --exp_name d=2 --model MLP_MHT_Corr5 --h 2048 --n_MHT_heads 4 --dropout_p 0.1 --lbd_L 5e-3 --lr_scheduler cyclic --log_interval 100 --lr 3e-5 --B_dist 8 --B_sample 1024 --n_MHT 1 --MMD_kernel linear --MMD_comp old --dim 2 --dataset gaussian_gaussian_centered --n_landmk 8
The same experiment can be done in different dimensions by changing --d.
To run the experiment, do:
python main_corr.py --N_iter 50000 --exp_name d=2 --model MLP_MHT_Corr4 --h 2048 --n_MHT_heads 4 --lbd_L 1e-3 --lr_scheduler cyclic --log_interval 100 --lr 3e-5 --B_dist 16 --B_sample 1024 --n_MHT 1 --MMD_kernel lap --dim 2 --dataset gaussian_gaussian_mixture --ggm_sigma_min 0.1 --ggm_sigma_max 0.8
The same experiment can be done in different dimensions by changing --d.
Run:
python main_corr.py --N_iter 200000 --exp_name mnist_example --dropout_p 0.1 --model MLP_MHT_Blocks_Corr --h 2048 --n_MHT_heads 4 --lbd_L 2e-2 --lr_scheduler cyclic --save_interval 50000 --log_interval 1000 --lr 3e-5 --B_dist 16 --MNIST_n_repeat 3 --n_MHT 2 --MMD_kernel multiscale --dim 2 --dataset MNIST --MNIST_noise 1e-2 --MNIST_single_digit false
Run:
python main_corr.py --N_iter 100000 --exp_name MHTblock=2_SIMP_d=20_lap_L=1e-3_B=8 --repeated_concat_t true --MHT_res_link true --I_quad simp --L_quad FD4_simp --t_batch_num 10 --model MFG_op_net --h 2048 --n_MHT_heads 4 --lbd_L 1e-3 --lbd_I 1e0 --lr_scheduler cyclic --log_interval 1000 --lr 3e-5 --B_dist 8 --B_sample 256 --n_MHT 2 --MMD_kernel lap --dim 20 --dataset crowd_motion --n_landmk 6 --dropout_p 0 --plot_x_min -5 --plot_x_max 5 --plot_y_min -5 --plot_y_max 5 --save_interval 100000 --L_comp grid --I_comp grid --MMD_comp old
Run:
python main_corr.py --N_iter 200000 --exp_name MHTblock=2_L=1e-3 --repeated_concat_t true --MHT_res_link true --I_quad simp --L_quad FD4_simp --t_batch_num 10 --model MFG_op_net --h 2048 --n_MHT_heads 4 --lbd_L 1e-3 --lbd_I 1e0 --lr_scheduler cyclic --log_interval 500 --lr 3e-5 --B_dist 4 --B_sample 256 --n_MHT 2 --MMD_kernel lap --dim 2 --dataset crowd_motion_two --n_landmk 6 --dropout_p 0 --plot_x_min -5 --plot_x_max 5 --plot_y_min -5 --plot_y_max 5 --save_interval 200000 --L_comp grid --I_comp grid --MMD_comp old
One can play with --lbd_L, --lbd_I to control the relative weights on the transport and interaction costs, respectively. For example, making --lbd_I larger encourages the agents to stay further away from the obstacle.