MDPNML: A Multidimensional Petri Net Markup Language Enabling Construction and Simulation of Comprehensive Digital Twin Models

A Digital Twin (DT) is a data-driven virtual representation of a physical system that updates in near-real-time and incorporates models of system physics and behaviors. Multidimensional Stochastic Petri Nets (MDSPNs), as an extension of traditional Stochastic Petri Nets (SPNs), provide an intuitive formalism for modeling and analyzing complex systems across multiple dimensions, enabling the development of comprehensive DTs. In MDSPNs, system objectives can be associated with different relevant dimensions, including time, energy, and waste. The Petri Net Markup Language (PNML), a standard XML-based interchange format, is widely used for sharing and executing Petri net models across tools. PNML, however, lacks multidimensional semantics. A PNML-compatible format for MDSPNs would enable portable model exchange across tools and allow conversion to time-oriented SPNs for generic PNML tools, supporting end-to-end traditional and comprehensive DT workflows. Such an extended PNML format also enhances model reproducibility and reduces the effort required to integrate dimension-specific behavior. In this paper, we introduce the Multidimensional Petri Net Markup Language (MDPNML) and identify necessary adaptations to the PNML format to represent MDSPNs. MDPNML supports multidimensional attributes, different dimensions in transitions, and simulation parameters for MDSPNs. Through an illustrative case study, we demonstrate MDPNML generation and execution for multidimensional simulation.