Petri Nets and Deep Petri Net for Simulation, Modeling and Analysis of Complex Systems

Abstract

The growing complexity of modern systems in fields such as artificial intelligence and large-scale simulations demands modeling approaches that are both expressive and formally analyzable. While Petri nets offer a solid foundation for modeling distributedsystems, they fall short in representing adaptive behaviors typical of ntelligent systems. This work introduces two complementary approaches to bridge this gap. The first extends classical Petri nets into a new formalism called Deep Petri Nets, integrating learning mechanisms inspired by neural networks. Three metamodels are defined using Eclipse Modeling Framework (EMF): the first for Petri nets, the second for neural networks, and the third for Deep Petri Nets, combining structural features of both. The second approach proposes a unified metamodel, NNPN (Neural Network of Petri Net), which merges Petri net and neural network elements into a cohesive model, later transformed into a Deep Petri Net. Model ransformations are achieved using Triple Graph Grammar (TGG) and Atlas Transformation Language (ATL) rules, ensuring consistency, traceability, and analytical capability. This dual-method framework supports the modeling of complex systems with both formal structure and adaptive behavior.