Multi-resolution modeling based on quotient space and DEVS

As simulation systems get more and more complex, the study of multi-resolution modeling (MRM) remains an exciting and fertile area of research. Contrasting its abundant successful use cases, a rigorous mathematical foundation is still lacking in MRM. In this paper, we propose a quotient space based multi-resolution modeling (QMRM) theory based on granular computing in artificial intelligence and on discrete-event system specification (DEVS) in modeling and simulation. Based on quotient sets, resolution, multi-resolution modeling and other related concepts are defined and a general concept framework is constructed. Based on the concepts of quotient set and natural projection, several MRM principles are derived. The internal consistency principle guarantees consistency among different perspectives of an atomic model, whereas the external consistency principle guarantees that different components in a coupled model are consistent. The false-preserving principle indicates that if a construction relation or state transformation relation of a component does not exist in a low resolution model, then the corresponding relations should not exist in its high resolution model. The true-preserving principle tells us that a high resolution model can be simplified by choosing the proper low resolution model. QMRM is not only a formal specification, but also a fundamental framework to understand MRM concepts, a guiding ideology to design specific MRM methods, and a modeling methodology to develop MRM systems. QMRM is created from a general simulation perspective, not limited by any specific application or problem domain aspects. The results of this paper can serve as a starting point for further study of multi-resolution problems in different domains.