A graph model and grammar for multi-scale modelling using XL

Abstract

A graph formalism and grammar suitable for multiscale modelling is introduced in this paper. Existing rule-based rewriting mechanisms related to L-systems do not take scales into account or rely on string-based mechanisms. This poses difficulties to develop multi-scale models using rule-based graph approaches. Using a type graph to capture scale relationships and accounting for scales using an additional edge type, we introduce a technique to overcome these problems. Syntax for expressing multi-scale graphs allows the construction of models in the language XL coupled with existing rule-based functionality.

An approach to multiscale modelling with graph grammars

“…If incomparable scales exist, a linear ordering is unsuitable for representation. In such cases, a generalized multiscale graph (Godin and Caraglio, 1998) or a structure-of-scales (Ong and Kurth, 2012) can represent the scales as a partially ordered set. Such refinement orderings (as seen in Fig.…”

“…2A) are potentially useful for models with an extensive range of scales. The structure-of-scales is one of the three algebraic structures proposed by Ong and Kurth (2012) that form a three-part graphbased data structure (Fig. 2).…”

“…For example, one scale may have leaf and internode types, while another, coarser scale 2. An illustration of the three-part graph data structure (Ong and Kurth, 2012) comprising a structure-of-scales (A), a type graph (B) and an instanced graph (C). The structure-of-scales (A) shows incomparability between the axes and the voxel space, but both refine to a common organ scale.…”

“…One can thus say that the refinement relationships between the types are controlled or restricted by the structureof-scales. [Some additional constraints are demanded for type graphs; see Ong and Kurth (2012) for a complete definition.] A type graph may contain circles (undirected closed paths in the sense of graph theory).…”

“…As indicated by Hanan (2013), one of the current challenges in FSPM is the extension of formalisms to support multiscale modelling. Corresponding to the notion of decomposition in L-systems (Prusinkiewicz et al, 2001) and multiscale representation of plant structures, recent developments have been made by Boudon et al (2012) to allow string-based grammar operations on MTG data structures and by Ong and Kurth (2012) to allow the operation of rules on multiscale typed graphs.…”