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Graph neural networks, which generalize deep learning to graph-structured data, have achieved significant improvements in numerous graph-related tasks. Petri nets (PNs), on the other hand, are mainly used for the modeling and analysis of various event-driven systems from the perspective of prior knowledge, mechanisms, and tasks. Compared with graph data, net data can simulate the dynamic behavioral features of systems and are more suitable for representing real-world problems. However, the problem of large-scale data analysis has been puzzling the PN field for decades, and thus, limited its universal applicability. In this article, a framework of net learning (NL) is proposed. NL contains the advantages of PN modeling and analysis with the advantages of graph learning computation. Then, two kinds of NL algorithms are designed for performance analysis of stochastic PNs, and more specifically, the hidden feature information of the PN is obtained by mapping net information to the low-dimensional feature space. Experiments demonstrate the effectiveness of the proposed model and algorithms on the performance analysis of stochastic PNs. [ABSTRACT FROM AUTHOR]

Graph contrastive learning has achieved rapid development in learning representations from graph-structured data, which aims to maximize the mutual information between two representations learned from different augmented views of a graph. However, maximizing the mutual information between different views without any constraints may cause encoders to capture information irrelevant to downstream tasks, limiting the efficiency of graph contrastive learning methods. To tackle these issues, we propose a Graph Contrastive Learning method with Min-max mutual Information (GCLMI). Specifically, we conduct theoretical analysis to present our learning objective. It designs a min-max principle to constrain the mutual information among multiple views, including between a graph and each of its augmented views, as well as between different augmented views. Based on the learning objective, we further construct two augmented views by separating the feature and topology information of a graph to preserve different semantic information from the graph. Subsequently, we maximize the mutual information between each augmented view and the graph while minimizing the mutual information between two augmented views, to learn informative and diverse representations. Extensive experiments are conducted on a variety of graph datasets, and experimental results show that GCLMI achieves better or competitive performance compared with state-of-the-art methods. [ABSTRACT FROM AUTHOR]