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.

中文翻译：

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用于解决平均场博弈的在线交互式物理信息对抗网络


我们提出了一种在线交互式物理信息对抗网络 （IPIAN），从物理信息交互的角度解决平均场博弈 （MFG）。在这项研究中，我们将代理之间的交互建模为一个基于物理学的交换过程，量化了个人策略选择的演变和分布。我们利用 MFGs 的变分二元结构将动态博弈问题转化为静态优化问题，随后采用对抗网络来解决平均场博弈。基于生成对抗框架，两个在线物理信息网络求解值和密度函数。这些网络经过训练，可以通过对抗性手段近似 MFG 的解。此外，引入了一种自我注意机制，以增强对战略物理信息的关注，从而提高 IPIAN 的表达能力。数值实验验证了 IPIAN 在求解高维平均场博弈模型方面的有效性，正如在各种场景中使用四旋翼飞行器进行的避障实验所证明的那样。