Modeling and simulation of multi-scale environmental systems with Generalized Hybrid Petri Nets

Abstract

Predicting and studying the dynamics and properties of environmental systems necessitates the construction and simulation of mathematical models entailing different levels of complexities. Such type of computational experiments often require the combination of discrete and continuous variables as well as processes operating at different time scales. Furthermore, the iterative steps of constructing and analyzing environmental models might involve researchers with different background. Hybrid Petri nets may contribute in overcoming such challenges as they facilitate the implementation of systems integrating discrete and continuous dynamics. Additionally, the visual depiction of model components will inevitably help to bridge the gap between scientists with distinct expertise working on the same problem. Thus, modeling environmental systems with hybrid Petri nets enables the construction of complex processes while keeping the models comprehensible for researchers working on the same project with significantly divergent educational background. In this paper we propose the utilization of a special class of hybrid Petri nets, Generalized Hybrid Petri Nets (GHPN ), to model and simulate environmental systems exposing processes interacting at different time-scales. GHPN integrate stochastic and deterministic semantics as well as some other types of special basic events. To this end, we present a case study illustrating the use of GHPN in constructing and simulating multi-timescale environmental scenarios.Keywords: modeling and simulation, Hybrid Petri Nets, multi-scale environmental systems, Chagas disease, Triatoma infestans IntroductionThe process of constructing and analyzing environmental systems is increasingly becoming a complex procedure (Seppelt et al., 2009;Uusitalo et al., 2015). On the one hand, it can require the amalgamation of different simulation techniques to accurately and efficiently find a solution to the problem under consideration (see e.g., Gillet, 2008;Gregorio et al., 1999). On the other hand, complex environmental systems require the collection and analysis of various data and information that cannot be tackled by researchers coming from just one area of expertise (Seppelt et al., 2009).While the ordinary differential equations (ODEs) approach is widely used to construct and simulate many problems in the environmental domain, certain classes of such problems cannot be adequately addressed using this approach alone. For instance in Khoury et al. (2013) construct a simple, but elegant ODEs model to study food and population dynamics in honey bee colonies. However, such a continuous approach cannot capture the effect of seasonal variations Herajy and Heiner GHPN for multi-scale environmental systems on many parameters. Contrary, in Schmickl and Crailsheim (2007) and Russell et al. (2013) a discrete simulation of recurrence and difference equations has been deployed to emulate the discrete changes in bee population taking into account seasonal variations. Nevertheless, certain scenarios necessitate ...

The Representation of Hydrological Dynamical Systems Using Extended Petri Nets (EPN)

“…The concept was originally presented in Carl Adam Petri's dissertation (Petri, 1966), and their early development and applications are found in reports that date back to the 1970s. PN became popular in theoretical computer science (Jensen & Kristensen, 2009), biology (Koch, 2010;Koch et al, 2010;Wilkinson, 2011), especially to represent parallel or concurrent activities (Murata, 1989), stochastic mechanics (Baez & Biamonte, 2012;Haas, 2006;Marsan et al, 1994), and to describe reaction networks (Gilbert & Heiner, 2006;Herajy & Heiner, 2015). In the case of reaction networks, clearly treated in Herajy and Heiner (2015),there are specific rules for computation, which are implicit in the PN structure used that do not lead to correct mass and energy budget equations.…”

“…Graphical representation has been fruitful in the sciences: The epitome is the case of Feynman diagrams in quantum electrodynamics (Kaiser, ), but representations of electrical circuits (Lohn & Colombano, ), stock‐flow diagrams of system dynamics models are also good examples (Takahashi, ) and reaction networks (Baez & Pollard, ; Herajy & Heiner, ) are also interesting examples. The resulting theories, informed by the diagrams, differed significantly from earlier approaches in the way the relevant phenomena were conceptualized and modeled.…”