Mean Field Game GAN

2021/03/14 by Shaojun Ma, Haomin Zhou, Ma, Shaojun +3
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2103.07855

openalex publication_date 2021/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a novel mean field games (MFGs) based GAN(generative adversarial network) framework. To be specific, we utilize the Hopf formula in density space to rewrite MFGs as a primal-dual problem so that we are able to train the model via neural networks and samples. Our model is flexible due to the freedom of choosing various functionals within the Hopf formula. Moreover, our formulation mathematically avoids Lipschitz-1 constraint. The correctness and efficiency of our method are validated through several experiments.

Citations

• Adam: A Method for Stochastic Optimization
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Two Numerical Methods for the elliptic Monge-Ampère equation

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