Scientific modeling is the process of generating abstract, conceptual, graphical and or mathematical models. Science offers a growing collection of methods, techniques and theory about all kinds of specialized scientific modeling.
Modeling is an essential and inseparable part of all scientific activity, and a lot of scientific disciplines have their own ideas about specific types of modeling. There is only little general theory about scientific modeling, offered by the philosophy of science, systems theory, and new fields like knowledge visualization.
Modeling is a comparatively new area of activity involving the marriage of ideas from various disciplines, and is an essential and inseparable part of all scientific activity. The professional modeler brings special skills and techniques to bear in order to produce results that are insightful, reliable, and useful. Modeling techniques include statistical methods, computer simulation, system identification, and sensitivity analysis. None of these, however, is as important as the ability to understand the underlying dynamics of a complex system. These insights are needed to assess whether the assumptions of a model are correct and complete. The modeller must be able to recognize whether a model reflects reality, and to identify and deal with divergences between theory and data.
One of the main aims of scientific modeling is to apply quantitative reasoning to observations about the world, in the hope of seeing aspects that may have escaped the notice of others. Now there are many specific techniques that modelers use, which enable us to discover aspect of reality that may not be obvious to everyone. One of the essentials is the understanding of the role that assumptions play in the development of the model. The usual approach to model development is to characterize the system, make some assumptions about how it works and translate these into equations and a simulation program. After simulation one of the final steps is the validation. The question if we can trust the data the model presented..
Scientific modeling basics
- Scientific method
- Scientific method refers to the body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. It is based on gathering observable, empirical and measurable evidence subject to specific principles of reasoning. A scientific method consists of the collection of data through observation and experimentation, and the formulation and testing of hypotheses.
- Scientific model
- A model is a physical, mathematical, or logical representation of a system entity, phenomenon, or process. It is a type of formal interpretation which deals with empirical entities, phenomena, and physical processes in a mathematical, or logical way.
- For the scientist, a model is also a way in which the human thought processes can be amplified.  Models that are rendered in software allow scientists to leverage computational power to simulate, visualize, manipulate and gain intuition about the entity, phenomenon or process being represented
- A simulation is the implementation of a model over time. A simulation brings a model to life and shows how a particular object or phenomenon will behave. It is useful for testing, analysis or training where real-world systems or concepts can be represented by a model. 
- Structure is a fundamental and sometimes intangible notion covering the recognition, observation, nature, and stability of patterns and relationships of entities. From a child's verbal description of a snowflake, to the detailed scientific analysis of the properties of magnetic fields, the concept of structure is an essential foundation of nearly every mode of inquiry and discovery in science, philosophy, and art.
- A system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole. The concept of an 'integrated whole' can also be stated in terms of a system embodying a set of relationships which are differentiated from relationships of the set to other elements, and from relationships between an element of the set and elements not a part of the relational regime.
- The process of generating a model
- Modeling refers to the process of generating a model as a conceptual representation of some phenomenon. Typically a model will refer only to some aspects of the phenomenon in question, and two models of the same phenomenon may be essentially different, that is in which the difference is more than just a simple renaming. This may be due to differing requirements of the model's end users or to conceptual or aesthetic differences by the modellers and decisions made during the modeling process. Aesthetic considerations that may influence the structure of a model might be the modeller's preference for a reduced ontology, preferences regarding probabilistic models vis-a-vis deterministic ones, discrete vs continuous time etc. For this reason users of a model need to understand the model's original purpose and the assumptions of its validity.
- The process of evaluating a model
- A model is evaluated first and foremost by its consistency to empirical data; any model inconsistent with reproducible observations must be modified or rejected. However, a fit to empirical data alone is not sufficient for a model to be accepted as valid. Other factors important in evaluating a model include:
- Ability to explain past observations
- Ability to predict future observations
- Ability to control events
- Cost of use, especially in combination with other models
- Refutability, enabling estimation of the degree of confidence in the model
- Simplicity, or even aesthetic appeal
- People may attempt to quantify the evaluation of a model using a utility function.
- Visualization is any technique for creating images, diagrams, or animations to communicate a message. Visualization through visual imagery has been an effective way to communicate both abstract and concrete ideas since the dawn of man. Examples from history include cave paintings, Egyptian hieroglyphs, Greek geometry, and Leonardo da Vinci's revolutionary methods of technical drawing for engineering and scientific purposes.
Types of scientific modeling
Business process modeling
In business process modeling the enterprise process model is often referred to as the business process model. Process models are core concepts in the discipline of process engineering. Process models are:
- Processes of the same nature that are classified together into a model.
- A description of a process at the type level.
- Since the process model is at the type level, a process is an instantiation of it.
The same process model is used repeatedly for the development of many applications and thus, has many instantiations.
One possible use of a process model is to prescribe how things must/should/could be done in contrast to the process itself which is really what happens. A process model is roughly an anticipation of what the process will look like. What the process shall be will be determined during actual system development.
Modeling and Simulation
One application of scientific modeling is the field of "Modeling and Simulation", generally referred to as "M&S". M&S has a spectrum of applications which range from concept development and analysis, through experimentation, measurement and verification, to disposal analysis. Projects and programs may use hundreds of different simulations, simulators and model analysis tools.
The figure shows how Modelling and Simulation is used as a central part of an integrated program in a Defence capability development process.
- List of computer graphics and descriptive geometry topics
- List of graphical methods
- Model (abstract)
- Modelling language
- Scientific visualization
- Seven Management and Planning Tools
- Systems Engineering
- Francis Neelamkavil (1987), Computer Simulation and Modeling, p.324.
- William Silvert (2001), Modeling as a Discipline, in: Int. J. General Systems Vol. 30(3), pp. 261.
- Isaac Newton (1687, 1713, 1726). " Rules for the study of natural philosophy", Philosophiae Naturalis Principia Mathematica, Third edition. The General Scholium containing the 4 rules follows Book 3, The System of the World. Reprinted on pages 794-796 of I. Bernard Cohen and Anne Whitman's 1999 translation, University of California Press ISBN 0-520-08817-4, 974 pages.
- scientific method, Merriam-Webster Dictionary.
- C. West Churchman, The Systems Approach, New York: Dell publishing, 1968, p.61
- Systems Engineering Fundamentals. Defense Acquisition University Press, 2001.
- Pullan, Wendy (2000). Structure. Cambridge: Cambridge University Press. ISBN 0521782589.
- C. Rolland, Modeling the Requirements Engineering Process, 3rd European-Japanese Seminar on Information Modelling and Knowledge Bases, Budapest, Hungary, June 1993.
- C. Rolland and C. Thanos Pernici, A Comprehensive View of Process Engineering. Proceedings of the 10th International Conference CAiSE'98, B. Lecture Notes in Computer Science 1413, Pisa, Italy, Springer, June 1998.
- Due to the fact that "Modeling and Simulation" is frequently taught in male dominated undergraduate environments, this field of application is deliberately named "Modeling and Simulation", rather than "Simulation and Modeling", to avoid distractions which may arise due to any possible association with the negative connotations of S&M.
Nowadays there are some 40 magazines about scientific modeling which offer all kinds of international forums. Since the 1960s there is a strong growing amount of books and magazines about specific forms of scientific modeling. There is also a lot of discussion about scientific modeling in the philosophy-of-science literature. A selection:
- Churchman, C. West (1968), The Systems Approach, New York: Dell Publishing.
- Silvert, William (2001), "Modelling as a Discipline", in: Int. J. General Systems Vol. 30(3), pp. 261-282.
- Frigg, Roman and Hartmann, Stephan (2006), Models in Science, in: Stanford Encyclopedia of Philosophy, 2006.
- Hegselmann, Rainer, Ulrich Müller and Klaus Troitzsch (eds.) (1996), Modelling and Simulation in the Social Sciences from the Philosophy of Science Point of View. Theory and Decision Library. Dordrecht: Kluwer.
- Humphreys, Paul (2004), Extending Ourselves: Computational Science, Empiricism, and Scientific Method. Oxford: Oxford University Press.
- Rohrlich, Fritz (1990) “Computer Simulations in the Physical Sciences”, in Proceedings of the Philosophy of Science Association, Vol. 2, edited by Arthur Fine et al., 507-518. East Lansing: The Philosophy of Science Association.
- Schnell, Rainer (1990), “Computersimulation und Theoriebildung in den Sozialwissenschaften”, Kölner Zeitschrift für Soziologie und Sozialpsychologie 1, 109-128.
- Sismondo, Sergio and Snait Gissis (eds.) (1999), Modeling and Simulation. Special Issue of Science in Context 12.
- Winsberg, Eric (2001), “Simulations, Models and Theories: Complex Physical Systems and their Representations”, Philosophy of Science 68 (Proceedings): 442-454.
- Winsberg, Eric (2003), “Simulated Experiments: Methodology for a Virtual World”, Philosophy of Science 70: 105–125.
- Models in Science. Entry in the Stanford Encyclopedia of Philosophy
- Research in simulation and modeling of various physical systems