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What are Models and Simulations (M&S)?
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A model is a representation of an entity and/or a process. The key word in this definition is "representation," for which we could also use "depiction." For physical models, like "model airplanes," it is easy to describe a model as a "depiction" of a real airplane. Some models are very good depictions and some are not as good. The first model airplane I built as a child looked a little like an airplane - but no one knew which real airplane the model represented. Contrast this to the airplane models I later helped build (as an aeronautical engineer) for wind tunnel testing - they were very good representations of specific airplanes; they were very good models. Another form of model is a mathematical model. Continuing the airplane example, aeronautical engineers can describe the shape of a wing mathematically using a set of equations that most people would not understand. These equations are mathematical models. Similarly, we teach high school geometry students how to represent a cylinder with a set of equations - these are mathematical models of a cylinder. In art class, we can teach students to craft a cylinder out of different materials - providing us with physical models of a cylinder. Therefore, for entities we can easily develop both physical and mathematical models. A representation of a process is harder to visualize. Let's take an example of a vehicle accelerating to 60 miles an hour and then holding that speed for a set amount of time. This is a two step process. We have mathematical models (from basic physics) that will provide the distance the vehicle has traveled at any point in time. The distance can be associated with a map to get an actual location at any point in time. This is a very simple process that can be represented with mathematical equations provided by physics. Not all physics-based mathematical models are this simple (or we would all be Nobel Prize winners in physics). However, the good news is that, after years of physics research, the derivation of physics-based mathematical models has rules and techniques that can be rigorously applied. The representation of physics- based processes can be derived systematically and can be validated by experts. There are many processes that we would like to model, but they are not physics-based. For example, a model of a country's economy could include factors such as rainfall, foreign imports of food products, GNP, inflation, etc. Unfortunately, we don't know the mathematical relationships among these factors and the thousands of other parameters that are important to economic processes. Therefore, developing an adequate mathematical representation (i.e. model) of the economic processes in a specific country is very challenging. It is possible to develop some simple representations with only a handful of key parameters, but just like the model airplane that I built as a child, it may not be recognizable as a representation of the economy of a real world country. Lastly, a simulation is a model or composite of models for which selected parameters are uniformly varied. In the most familiar simulations, the parameter that changes uniformly is time. At least one equation in the model has time as a variable and as it changes, the changes to all the other variables automatically occur because all the equations are linked. When we want to simulate a process that does not have standard rules like the laws of physics and for which there are factors that we don't understand, there are no "correct" equations that can be systematically derived. Equally difficult, when we want to simulate a process that has human beings making decisions, we have to have ways to represent cognitive processes.
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In summary, a model or simulation is only as good as the understanding we have of the entity or process we want to represent and our ability to convert that understanding into mathematical models.
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