Scientific modelling 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 modelling. Also a way to read elements easily which have been broken down to the simplest form

Modelling is an essential and inseparable part of all scientific activity, and many scientific disciplines have their own ideas about specific types of modelling. There is little general theory about scientific modelling, offered by the philosophy of science, systems theory, and new fields like knowledge visualization.

Modelling is a comparatively new area of activity involving the marriage of ideas from various disciplines^[1], and is an essential and inseparable part of all scientific activity. The professional modeller, according to Silvert,^[2] brings special skills and techniques to bear in order to produce results that are insightful, reliable, and useful. Modelling 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.^[2]

One of the main aims of scientific modelling, according to Silvert,^[2] is to apply quantitative reasoning to observations about the world, in the hope of seeing aspects that may have escaped the notice of others. There are many specific techniques that modellers use, which enables one to discover aspects 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; i.e. determining whether the results produced by the model can be trusted.^[2]

A model is a simplified abstract view of the complex reality. A scientific model represents empirical objects, phenomena, and physical processes in a logical way. Attempts to formalize the principles of the empirical sciences in the same way logicians axiomatize the principles of logic use an interpretation to model reality. The aim of these attempts is to construct a formal system for which reality is the only interpretation. The world is an interpretation (or model) of these sciences, only insofar as these sciences are true.^[3]

For the scientist, a model is also a way in which the human thought processes can be amplified.^[4] 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.

Models are typically used when it is either impossible or impractical to create experimental conditions in which scientists can directly measure outcomes. Direct measurement of outcomes under controlled conditions (see Controlled Experiment, Scientific Method) will always be more accurate than modeled estimates of outcomes. When predicting outcomes, models use assumptions, while measurements do not. As the number of assumptions in a model increases, the accuracy and relevance of the model diminishes.

A modelling language is any artificial language that can be used to express information or knowledge or systems in a structure that is defined by a consistent set of rules. The rules are used for interpretation of the meaning of components in the structure. Examples of modelling languages are the Unified Modeling Language (UML) for software systems, IDEF for processes and the VRML for 3-D computer graphics models designed particularly with the World Wide Web in mind.

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.^[5]

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.^[6]

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.

Modelling 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 modelling 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^{[citation needed]}.

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:^{[citation needed]}

• Ability to explain past observations
• Ability to predict future observations
• 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.

In business process modelling 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.^[8]

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• Analogical modelling
• Assembly modelling
• Catastrophe modelling
• Choice Modelling
• Climate model
• Continuous modelling
• Data modelling
• Document modelling
• Discrete modelling
• Economic model
• Ecosystem model

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• Empirical modelling
• Enterprise modelling
• Futures studies
• Geologic modelling
• Goal Modelling
• Homology modelling
• Hydrogeology
• Hydrography
• Hydrologic modelling
• Informative Modelling
• Mathematical modelling

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• Metabolic network modelling
• Modelling in Epidemiology
• Molecular modelling
• Modelling biological systems
• Multiscale modeling
• NLP modelling
• Predictive modelling
• Simulation
• Software modelling
• Solid modelling
• Statistics
• Stochastic modelling
• System dynamics

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One application of scientific modelling is the field of "Modeling and Simulation", generally referred to as "M&S".^[9] 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.^[5]

• List of computer graphics and descriptive geometry topics
• List of graphical methods
• Modelling language
• Scientific visualization
• Seven Management and Planning Tools
• Simulation
• Systems Engineering
• Toy model

Nowadays there are some 40 magazines about scientific modelling 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 modelling. There is also a lot of discussion about scientific modelling in the philosophy-of-science literature. A selection:

• C. West Churchman (1968). The Systems Approach, New York: Dell Publishing.
• Rainer Hegselmann, 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.
• Paul Humphreys (2004). Extending Ourselves: Computational Science, Empiricism, and Scientific Method. Oxford: Oxford University Press.
• Johannes Lenhard, Günter Küppers and Terry Shinn (Eds.) (2006) "Simulation: Pragmatic Constructions of Reality", Springer Berlin.
• Fritz Rohrlich (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.
• Rainer Schnell (1990). "Computersimulation und Theoriebildung in den Sozialwissenschaften". In: Kölner Zeitschrift für Soziologie und Sozialpsychologie 1, 109-128.
• Sergio Sismondo and Snait Gissis (eds.) (1999). Modeling and Simulation. Special Issue of Science in Context 12.
• Eric Winsberg (2001). "Simulations, Models and Theories: Complex Physical Systems and their Representations". In: Philosophy of Science 68 (Proceedings): 442-454.
• Eric Winsberg (2003). "Simulated Experiments: Methodology for a Virtual World". In: Philosophy of Science 70: 105–125.

Wikimedia Commons has media related to Scientific modeling.

• Models in Science. Entry in the Stanford Encyclopedia of Philosophy
• The World as a Process: Simulations in the Natural and Social Sciences, in: R. Hegselmann et al. (eds.), Modelling and Simulation in the Social Sciences from the Philosophy of Science Point of View, Theory and Decision Library. Dordrecht: Kluwer 1996, 77-100.
• Research in simulation and modeling of various physical systems
• Modeling Water Quality Information Center, U.S. Department of Agriculture