Physics-informed adversarial networks for stochastic second-order mean-field games of autonomous traffic

Inspired by the highly complex and nonlinear traffic flow phenomenon, we propose a second-order continuum model for autonomous vehicles (AVs) by considering them as rational and utility-optimizing agents. Further, by accounting for stochastic fluctuations in driving dynamics, a non-cooperative differential game problem is converted to a mean-field game (MFG) system comprising a forward-in-time second-order continuity equation (CE) and a backward-in-time parabolic Hamilton–Jacobi–Bellman (HJB) equation. By formulating various driving cost functions, we generate two non-separable stochastic MFG systems. Next, a modified generative adversarial network (GAN)-based machine learning (ML) model is proposed as a surrogate to learn the dynamics of the proposed MFG systems. The proposed GAN comprises three physics-informed neural networks (PINNs) that compete with each other until an approximate equilibrium is attained. We validate our results on both the simulated and real-world datasets.