Scientific modeling

A modeling is the most basic learning task of acquiring the ability to organize information about the world into a useful structure. A model is a systematic description of an object or phenomenon (event or process) that shares important characteristics with its real-world counterpart and supports its detailed investigation. A modeler may be a researcher, a inventor, a designer, a teacher or an artist. Models are commonly represented as a system of postulates, data, and inferences presented visually, in material form, in mathematical terms, or as a computer simulation. Scientific models invariably involve some degree of idealization, abstraction, or fictionalization of their target system e.g., the Bohr model of the atom, the Lorenz model of the atmosphere, and the Lotka-Volterra model of predator-prey interaction.  Models can perform two fundamentally different representational functions. A model can be a representation of a selected part of the world (the ‘target system’). Depending on the nature of the target, such models are either models of phenomena or models of data. On the other hand, a model can represent a theory in the sense that it interprets the laws and axioms of that theory.  Simply a scientific model is a representation of a system (e.g., the solar system) or a phenomenon (e.g., the oxidation of metal, or thermoregulation in humans). These representations can take the form of pictorials-drawings, diagrams, flow charts, equations, graphs, computer simulations, or even physical objects.

Definition

A model is a formal, abstract, hypothetical  description of a complex entity, system or process. Scientific models can be material, visual, mathematical or computational and are often used in the construction of scientific theories.  Models are representational system for observable and unobservable features of an entity or process. The term model is derived from Latin, modus/modulus meaning ‘little measure.’

Types of scientific models

There are two major types of models: Qualitative models often use verbal descriptions of general behavior. Quantitative models express units of analyses, their interrelations and dynamics using properties susceptible of measurement. Generally, 3 types of models used in science are physical models, mathematical models and conceptual models.

Physical or material model is a smaller or larger physical copy of an object e.g., Watson and Crick’s model of DNA, architectural model of a building, wooden models of bridges, planes or ships.

Mathematical model is a description of a system using mathematical concepts and languages. They are usually composed of relationships and variables. In other words, a mathematical model is one constructed using mathematical concepts such as constants, variables, functions, equations etc.

Conceptual or symbolic model is a descriptive model of a system that is based on qualitative assumptions about its elements, their relationships and system boundaries. It may be a set of concepts with propositions that describe them, express the relationships between them or set forth the basic assumptions of the model e.g., process flow models, data flow models, logical data model.

Other categories of models

Deductive models vs. inductive models

 Deductive models take a “top-down” approach by working from the more general to the more specific. Deduction can be seen as the identification of an unknown particular based on the resemblance of the particular to a set of known facts. Inductive models takes a "bottom up" approach that starts with specific observations and measures, continues with the identification of patterns and regularities, then formulates some tentative hypotheses that can be explored, and results in general conclusions or theories.

Deterministic models vs. stochastic models

Deterministic models describe the behavior of an object or phenomenon whose behavior is entirely determined by its initial state and inputs. e.g., Newton's laws can be used to describe and predict planetary motion. Stochastic or probabilistic models make it possible to predict the behavior of an object or phenomenon if the influence of several unknown factors is sizable—the subsequent state is determined both by predictable actions and by a random element.

Descriptive models vs. process models

Descriptive models aim to describe the major features of typically static data sets. Results are communicated via tables, charts, or maps. Process models aim to capture the mechanisms and temporal dynamics by which real-world networks are created. Computational models describe the structure of dynamics of science using different computational approaches such as agent based modeling, population models, cellular automata, or statistical mechanics.

Universal models vs. domain specific models
Universal models aim to simulate processes that hold true across different domains and data sets. Domain specific models aim to replicate a concrete data set in a given domain.

Iconic models (true models) – are large or small scale representation of states, objects or events. An iconic model is a truthful mirror image of the target except a transformation in scale e.g., road maps, pilot plant, aerial photograph.

Idealized model- is a deliberate simplification of something complicated with the objective of making it more tractable e.g., Philips curve in economics which specifies a relationship between inflation and unemployment.

Analogical models - is based on shared properties or relevant similarities between two things e.g., the hydraulic model of an economic system, the billiard ball model of a gas.

Phenomenological models - models that only represent observable properties of their targets and refrain from postulating hidden mechanisms and the like.

Steps in developing scientific models

Modeling is a process of selection and transformation. Selection firstly of what to represent that is to say defining the prototype and then of a set of characteristics of the prototype to be incorporated after appropriate transformation in the model.  It involves 4 steps:

Planning – this requires a clear definition of the problem.  The problem definition will establish a definite objective for analysis. This objective is invaluable in outlining a path from the problem to the solution. Are we interested in the process? What is our main concern? What is the appropriate response or dependent variable? What are the relevant explanatory or independent variables?

Data collection – this requires the Identification of response and explanatory variables. This is followed by predictions, extrapolations and interpolations of the problem.

Model fitting – different models which relate the response variable to the explanatory variables is tested to see how well they fit the experimental data.

Model validation – the model is evaluated using the experimental data not used in building the model.

Basic needs for modeling

One chooses to use a model under three situations.    

1. It is too complicated, expensive, dangerous or inconvenient to work with the prototype.
2. Complex situations are often difficult to grasp, difficult to describe and difficult to discuss.
3. There are situations in which a model may serve to generate variety.

Characteristics of good models

Keeping ideas simple – a good model use simple notations and represent the system with few rules and symbols.
Reliability – one can apply a model on a number of different occasions and the chosen model has to reliably reflect the behaviour of the system.
Validity – a model should reflect/ measure the dynamics of a system which it is supposed to reflect or measure.

Uses of models

Models are fundamental elements in learning about the world. Models give rise to a new style of reasoning, so-called ‘model based reasoning.’ Learning with models happens in three stages: denotation (representation of relation between the model and the target), demonstration (exhibiting certain theoretical claims about its internal constitution or mechanism), and interpretation/explanation (claims about the target system).

Models are used as partial substitutes for their prototypes to assist in designing, understanding, predicting the behavior, controlling or experiencing emotions associated the prototype.

A skilfully designed and constructed model can be a powerful means of communication.

Model is a tool to be used by the design team both to test the appropriateness of their plans and to assist in translating the final design into actuality. Often in the process of design, a series of models will be constructed each of which is intended to provide information on a particular aspect of the behavior of the prototype. Modelling is often the most appropriate research procedure.