An online interactive physics-informed adversarial network for solving mean field games

We propose an online interactive physics-informed adversarial network (IPIAN) to address mean field games (MFGs) from the perspective of physics-informed interaction. In this study, we model the interaction between agents as a physics-informed exchange process, quantifying the evolution and distribution of individual strategy choices. We utilize the variational dyadic structure of MFGs to transform the dynamic game problem into a static optimization problem, subsequently employing the adversarial network to solve the mean field games. Based on the generative adversarial framework, two online physics-informed networks solve the value and density functions. These networks are trained to approximate the solution of MFGs through adversarial means. Additionally, a self-attention mechanism is introduced to enhance the focus on strategic physics-informed, thereby improving the expressiveness of IPIAN. Numerical experiments validate the effectiveness of IPIAN in solving high-dimensional mean field game models, as demonstrated by obstacle avoidance experiments with a quadrotor in various scenarios.