The Multiresolution Multiperspective Modeling Education Essay

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Several researchers Davis and Bigelow 1998; Davis 2000; Yılmaz and oren 2004; Baohong and Kedi 2004; Yılmaz et al. 2007; Davis and Tolk 2007 have explored the issues involved in the construction of multiresolution multiperspective models. This section of the proposal offers an overview of these existing studies with special emphasis on feasibility concerns and limitations.

Background on Multimodeling

Providing variable levels of abstractions and perspectives focusing on different aspects of a system is an important yet challenging task. Most of the real world phenomena can be described in many different ways and trying to understand such phenomena often requires the use of a set of complementary models that together are able to describe the whole process (Ã-ren 1987, 1991; Zeigler et al. 2000; Yılmaz and Ã-ren 2004).

Several studies like multifaceted, multiparadigm (Zeigler and Ã-ren 1986; Fishwick and Zeigler 1992) and multiresolution modeling (MRM) (Davis and Bigelow 1998) have explored the solution space to layout a common framework to have a better understanding of the challenges in developing advanced simulation modeling infrastructures that can cope with uncertainty and multilevel system description. In general terms, a multimodel (MM) is a modular model in which there are submodels representing different parts of the model (Yılmaz and Ã-ren 2004).

Yılmaz and Ã-ren (2004) categorize the MMs into two general groups based on their structures and behaviors (see Table 2 : Basic definitions and brief explanations of the envisioned multimodel types (Yılmaz and Ã-ren 2004)). The second level decomposition of the MMs is called ''decomposition based on additional criteria.'' There are four different additional criteria: number, variability, nature of knowledge and location of knowledge. ''Number'' criteria describes the how many submodels are active at the run time. If only one model is active at a time, then it is categorized as a Single Aspect (one submodel that describes on point of view) MM (or sequential MM). Otherwise, the model will be considered as a Multiaspect MM since there is at least more than one model is active at a time. ''Variability'' criteria describes whether the submodels are statically or dynamically generated. ''Nature of knowledge'' criteria describe the reason behind to make transition between the submodels in a MM. These transitions can take place under some certain constraints; or patterns that repeatedly occur within a system triggers the transition; or the transitions occur to achieve a certain goal (goal directing the submodel transition rule and goal-directed submodel transition mechanism should be specified). Finally, ''location of knowledge'' criteria describes the location of the information source which is necessary to make transition between the submodels in a MM. The necessary information can be provided externally or this information can be within the submodel.

Table 2 : Basic definitions and brief explanations of the envisioned multimodel types (Yılmaz and Ã-ren 2004)

All of the existing proposals have a common goal of providing a generic modeling framework for constructing different models at different levels of abstraction of different perspectives. However, there exist number of important feasibility concerns and limitations in these studies that are also underlined by several authors (Bigelow and Davis 2003; Tolk and Davis 2007; Yilmaz et al. 2007):

The lack of emphasis put on synchronizing pre-existing models from different perspectives.

The lack of fundamental requirements and design principles, resulting in application specific models at different resolutions or different perspectives.

The lack of a unified and coherent framework, resulting in statically defined models at different resolutions. In other words, lack of dynamic model updating.

The lack formal specifications which make it difficult to establish a common language among different researchers and model developers.

These feasibility concerns and limitations show us the gaps in the existing works and help us to form our research objectives and questions. Moreover, as we pointed out earlier in this section, understanding of conceptual assumptions and constraints remains the pivotal element for success.

Exploring the Multi-resolution Multi-perspective Modeling Approach

In the light of these existing studies, Davis (2000) proposed a methodology named multiresolution multiperspective modeling (MRMPM) which is concerned with resolving the representational and conceptual difference among models that are joined to satisfy a common objective. They define their modeling approach as the process of constructing models, model families or both, for providing a variety of resolutions and perspectives. In their MRMPM context, a set of models of the same entity forms a model family. In a model family, models are not isolated from each other; instead they are assumed to be highly related and consistent. Therefore, this consistency allows different models to be coordinated during the running of multiresolution models.

In order to sweep the clouds away a little bit, it is better to talk about Davis and Bigelow's MRM (1998) approach since MRM provides the basis of for MRMPM. According to the definition of Davis (2000), ''MRM is the process of building a single model, a model family or both to describe the same phenomena at different levels of resolution, and to allow users to input parameters at those different levels depending upon their needs.'' In the MRM context, Davis and Tolk (2007) define the term resolution as the level of granularity with which the concept is presented. The term resolution will be discussed in Section 2.3 in detail.

MRM is a highly applicable and effective way of dealing with complexity and handling composability (Davis and Tolk 2007). Composability, in here, is the capability of collecting the right components and joining them together in different combinations to complete a set of predefined user requirements (NRC 2006). MRM has the goal to build models at various levels of detail, which are related with each other in a way that each model provides different levels of understanding about the same phenomenon in a system. It is important to have these different levels of details, since traditional way of dealing with complex systems (as we already mentioned earlier in this section) assumes (or requires) that a ''natural decomposition'' of a system is possible and it forms the hierarchical structure of the system (Davis and Bigelow 1998).

The fundamental concepts of having models at various levels of details have been studied and published by several researchers (Davis and Huber 1992; Davis and Hillestad 1993; Reynolds et al. 1997) as a result of the multifaceted, multiparadigm studies (Zeigler and Ã-ren 1986; Fishwick and Zeigler 1992). Another important contribution to M&S in terms of having models at different hierarchical levels is Fishwick's hierarchical reasoning (1986, 1995). Further, from a top-down approach, MRM not only enables the understanding of decomposition of a system into subsystems but it also has the ability to provide the bottom-up meaning of the phenomena to the user (Davis and Tolk 2007). MRM helps the designer to form information at different levels of details based on the user requirements. It provides better control and understanding to the users about a real-world phenomenon by allowing him/her to zoom in and zoom out to the model.

Although having different levels of details can be a very useful property, one should not forget that these levels of details are generated through a point of view. Point of view, in here, should be understood as the need for having different model representations and there is no single way to model a real world phenomenon. Every actor can model the same phenomenon with his/her own perception which may differ from another. This results in the need of defining a new concept to describe the purpose of each model.

For that reason, Davis and Bigelow introduce the notion of ''perspective'' (which will be further discussed in Section 2.4) to Davis to their MRM approach and propose the MRMPM (2002). They describe the need of introducing the ''perspective'' notion as: ''MRM allows users to change the resolution of models for looking at outputs, specifying inputs and reasoning about cause-effect relationships while multiperspective modeling allows users to change ''perspective'' as in choices of variables and their state spaces. Therefore, theoretically, MRMPM supposedly provides all these functionalities (Davis and Bigelow 2002).'' However, this needs further investigation as the two approaches haven't been represented in formal specifications and the existing highly abstract definitions don't have a common ground to make comparison. For that reason, the difference between MRM and MRMPM seems still vague (Baohong and Kedi 2004).

So far, we have basically discussed about the multimodeling studies which provide the preliminary ideas to the development of exploratory MRM and MRMPM approaches of Davis and Bigelow, and we have provided the definitions of these two approaches. However, in order to get a better grip on MRM and MRMPM approaches, we need clear and precise definitions of the key concepts like resolution, consistency and validity inside these MRM and MRMPM contexts. Following sections will provide the existing definitions in the literature from different authors.


All models are abstractions of reality, but some have more detail than others (Davis and Tolk 2007). Detail depends on scope: the extent of the system, input domain, and output range treated; and on resolution. Resolution defines the level of detail of system variables (Davis and Bigelow 1998). While fairly standard, this definition of resolution is ambiguous due to the fact that the resolution is context dependent and every variable of a model may have its own resolution. One model may be low resolution in one point of view and high resolution in another. Therefore, it is meaningful to accept that the resolution has many components as shown in Figure 2 : Dimensions of Resolution (Davis and Bigelow 1998).


Figure 2: Dimensions of Resolution (Davis and Bigelow 1998)

For example, a model may have higher resolutions because it deals with more fine-grained entities. In another point of view, a model may higher resolution than another model with the same entities because it ascribes to those entities a richer set of attributes. Or, a model with the same entities and attributes may have higher resolution because it describes the relationship among those attributes in more detailed way (e.g., one model may provide spatial information of trains in a map with their positions in latitudes, longitudes, while another model may use an abstract concept to expressed the train is in the station or not).

High resolution models are mostly used to make in-depth and provide relations between the variables in a more structural way than low resolution ones. However, only having a high resolution model may have its limitation on the scope of the system when answering strategic questions. Such pros and cons also exist for low resolution models. Low resolution models are less expensive to create, maintain and use, good for quick turn-around analysis, and they provide analytical agility with respect to the higher resolution ones in order to provide an operational overview of systems (Davis and Bigelow 2003). We can simply consider that the low resolution models are the match for low detailed cognitive interpretation of the detailed concepts. For example, statistical models can be considered as low resolution models when considering that they are obtained by applying statistical methods to the experiments conducted in high resolution models. The purpose is to create a general outline of a model by applying statistical methods to the high resolution models. However, advantages and weaknesses exist for both types of models; therefore, providing models of a real world phenomenon at different resolutions can be quite beneficial to a user.


In the traditional way to deal with complexity, it is assumed that the system is ''nearly decomposable'' which results in a hierarchical representation of the system (Simon 1962). However, one must realize that a hierarchical decomposition can only be done once a perspective has been chosen. When modeling a system, this assumption is also exists.

Models are purposeful abstractions of reality and as such different abstractions serving different purposes can be used to describe the same reality (Davis and Anderson 2003). Since there is no single correct way to conceptualize reality, there is no single way to design a multi resolution model of a system. In other words, a given system can be described from different perspectives, much as physics models can have alternative representations (Davis and Tolk 2007). Davis and Bigelow (2002), therefore, introduced the notion of perspective in their MRMPM approach after they introduced the MRM (1998) as the need of having different model representations.

Different perspectives correspond to different decompositions of the system. Therefore, it would allow us to understand some of the complex real-world phenomenon that cannot be understood within a single perspective. Having multiple perspectives of a system is very useful to understand the big picture (for example, a design problem that requires integrating financial, operational and environmental perspective at the same time).

Therefore, the ability to create a linkage between each perspective, if possible, is essential to have a multiperspective modeling framework. It requires that either the models that already exist or generated are needed to be consistent with each other. Therefore, one of the things that need to be further investigated is the feasibility of employing multiple perspectives.

Consistency and Validation

So far, we have discussed about the high and low resolution models which constitute the multiresolution modeling families in the MRM context introduced by Davis and Bigelow. In doing so, we have relied on an intuitive notion of consistency between models with different levels of resolution. One can understand intuitively that a multiresolution model family displays consistency if employing its family members at different levels of resolution generates no contradictions (Davis and Bigelow 2002). In this section, we will try to describe a more precise notion of consistency.

Multi-resolution model families need to be capable of simultaneously operating at different levels, while maintaining consistency at each level of abstraction (Yılmaz et al. 2007). Challenges involved in assuring consistency across levels of resolutions are explored in (Reynolds et al. 1997). It has been argued that designing models at different levels of resolution requires principled design strategies that take potential discrepancies into account (Reynolds et al. 1997; Davis 2000). While the observations presented in (Reynolds et al. 1997) are generally applicable, the presented design strategy is overly simplistic. The design involves a Multi-resolution Entity (MRE) that encapsulates a specific number of entities, each with its own state information. Dynamically updating entities in a given resolution level is not addressed in the MRE design scheme. However, exploring Course of Actions (COAs) with different models require seamless update of individual components at selected resolution levels.

In principle, we should use an even more general definition of consistency. Since resolution is multidimensional (it depends on system variables and the number of distinct states), one model of a pair could have higher resolution in one dimension, and the other could have higher resolution in a second dimension (This dimensions will be discussed in the Section 3.3.2). Therefore, the order of models (in terms their order of resolution) should be carefully studied.

Another question that need to be answered when designing a model is whether the model valid or not. Issues of validity are always present for models but for models that combine different levels of resolutions, there can be several issues that need to be considered: Assumptions when creating the model may be wrong; Moreover, the logic or calculations used may be wrong, or both. For example; if someone built a model of a railway network that he regarded as better or more interesting than the ones already available, that model could be ''plugged in'' and run as a black box. However, it might or might not correspond to something that could be followed in the real world. For example, such a model might have exploited some weakness in the railway simulation by using some probabilities that would prove superior in the simulation but would, in the real world, be ruled out by factors not explicitly in the model. Further, and also very important in our case, a model that is adequately valid in one context may not be valid in another-even if the assumptions are taken care of (Davis and Tolk 2007).

Validity issues because of the composition of models can even be studied at a formal level. Weisel, Petty, and Mielke (2003) have done so and demonstrated difficult issues. Tolk (1999) gives a number of examples in which the composition of valid federates into a federation doesn't ensure validity of the final result.

Towards Multiresolution Multiperspective Modeling (MRMPM)

Having new models for every different perspective often requires too much money and time. Moreover, different models which are already built for a specific requirement may be quite useful in a new context, but should be organized in such a way that the output would be meaningful for the new purposes. Otherwise, they can't be combined into a multimodel. This may results in different models with minor changes or distinct models which has no meaningful relations between them. This is a waste of resources for the organizations.

MRMPM should allow the user to decide what resolution and perspective he or she wants, let the user enter a scenario (or data) to the model, execute the generated model and analyze the results at the time of use. In the light of this ideal, either the generated or pre-existing models should provide consistency with each other even though the models may vary based on the resolutions or perspectives. In other words, two models of the same entity at different resolution needs to validate each other. In order to do that, the consistency mentioned in Section 2.6 should be provided among the generated models or already existing models in a model family. It is obvious that the inputs (data or scenarios) will diverge based on the models' properties. For example, one can not input a detailed scenario to find an answer for a complex question to a simple model but can hope to predict certain aggregated behavior from an aggregated model instead of being burdened by an enormous program requiring very complex and detailed data input.