Ademovic Tahirovic Alma, Angeli David, Tahirovic Adnan, Strbac Goran
Department of Electrical and Electronic Engineering, Imperial College London, SW7 2AZ, London, UK.
Intelligent Systems Hub, 71000, Sarajevo, Bosnia and Herzegovina.
Sci Rep. 2025 May 20;15(1):17540. doi: 10.1038/s41598-025-01856-9.
Graphs are widely used to model interconnected systems, offering powerful tools for data representation and problem-solving. However, their reliance on pairwise, single-type, and static connections limits their expressive capacity. Recent developments extend this foundation through higher-order structures, such as hypergraphs, multilayer, and temporal networks, which better capture complex real-world interactions. Many real-world systems, ranging from brain connectivity and genetic pathways to socio-economic networks, exhibit multimodal and higher-order dependencies that traditional networks fail to represent. This paper introduces a novel generalisation of message passing into learning-based function approximation, namely multimodal heterogeneous network flow, which models information propagation across different semantic domains under conservation constraints. This framework is defined via Petri nets, which extend hypergraphs to support concurrent, multimodal flow and richer structural representation. Building on this foundation, we present the Petri Graph Neural Network (PGNN), a new class of graph neural networks capable of learning over higher-order, multimodal structures. PGNN generalises message passing by incorporating flow conversion and concurrency, leading to enhanced expressive power, interpretability, and computational efficiency. The work opens new directions in learning over complex structures, transcending transformer-based and traditional hypergraph-based algorithms. We validate results through theoretical analysis and real-world experiments, while demonstrating superior performance in, e.g., stock market prediction.
图被广泛用于对互联系统进行建模，为数据表示和问题解决提供了强大的工具。然而，它们对成对、单一类型和静态连接的依赖限制了其表达能力。最近的发展通过高阶结构扩展了这一基础，例如超图、多层网络和时间网络，这些结构能更好地捕捉复杂的现实世界交互。许多现实世界的系统，从大脑连接和遗传通路到社会经济网络，都表现出传统网络无法表示的多模态和高阶依赖性。本文介绍了一种将消息传递推广到基于学习的函数逼近的新方法，即多模态异构网络流，它在守恒约束下对跨不同语义域的信息传播进行建模。这个框架是通过Petri网定义的，Petri网扩展了超图以支持并发、多模态流和更丰富的结构表示。在此基础上，我们提出了Petri图神经网络（PGNN），这是一类能够对高阶、多模态结构进行学习的新型图神经网络。PGNN通过合并流转换和并发来推广消息传递，从而提高了表达能力、可解释性和计算效率。这项工作为复杂结构的学习开辟了新方向，超越了基于Transformer和传统基于超图的算法。我们通过理论分析和实际实验验证了结果，同时在例如股票市场预测中展示了卓越的性能。
