Shuo Liu

Mean-field games (MFGs) are developed to model the decision-making processes of a large number of interacting agents in multi-agent systems. This paper studies mean-field games on graphs ($\mathcal{G}$-MFGs). The equilibria of $\mathcal{G}$-MFGs, namely, mean-field equilibria (MFE), are challenging to solve for their high-dimensional action space because each agent has to make decisions when they are at junction nodes or on edges. Furthermore, when the initial population state varies on graphs, we have to recompute MFE, which could be computationally challenging and memory-demanding. To improve the scalability and avoid repeatedly solving $\mathcal{G}$-MFGs every time their initial state changes, this paper proposes physics-informed graph neural operators (PIGNO). The PIGNO utilizes a graph neural operator to generate population dynamics, given initial population distributions. To better train the neural operator, it leverages physics knowledge to propagate population state transitions on graphs. A learning algorithm is developed, and its performance is evaluated on autonomous driving games on road networks. Our results demonstrate that the PIGNO is scalable and generalizable when tested under unseen initial conditions.

Vulnerability identification is crucial to protect software systems from attacks for cyber-security. However, huge projects have more than millions of lines of code, and the complex dependencies make it hard to carry out traditional static and dynamic methods. Furthermore, the semantic structure of various types of vulnerabilities differs greatly and may occur simultaneously, making general rule-based methods difficult to extend. In this paper, we propose \textit{Vignat}, a novel attention-based framework for identifying vulnerabilities by learning graph-level semantic representations of code. We represent codes with code property graphs (CPGs) in fine grain and use graph attention networks (GATs) for vulnerability detection. The results show that Vignat is able to achieve $57.38\%$ accuracy on reliable datasets derived from popular C libraries. Furthermore, the interpretability of our GATs provides valuable insights into vulnerability patterns.