View source for Scientific modelling

{{Short description|Scientific activity  that produces models}}
{{Use British (Oxford) English|date=August 2016}}
[[File:Atmosphere composition diagram-en.svg|thumb|320px|Example scientific modelling. A schematic of chemical and transport processes related to atmospheric composition.]]
{{Research}}
'''Scientific modelling''' is an activity that produces [[model]]s representing [[empiricism|empirical]] objects, phenomena, and physical processes, to make a particular part or feature of the world easier to [[Understanding|understand]], [[Definition|define]], [[quantification (science)|quantify]], [[Visual system|visualize]], or [[Simulation|simulate]]. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features. Different types of models may be used for different purposes, such as [[conceptual model]]s to better understand, operational models to [[operational definition|operationalize]], [[mathematical model]]s to quantify, [[computational models]] to simulate, and [[graphical model]]s to visualize the subject. 

Modelling is an essential and inseparable part of many scientific disciplines, each of which has its own ideas about specific types of modelling.<ref>Cartwright, Nancy. 1983. ''[http://www.generativescience.org/papers/nature/Cartwright-_1983.pdf How the Laws of Physics Lie]''. Oxford University Press</ref><ref>Hacking, Ian. 1983. ''Representing and Intervening. Introductory Topics in the Philosophy of Natural Science''. Cambridge University Press</ref> The following was said by [[John von Neumann]].<ref>von Neumann, J. (1995), "Method in the physical sciences", in Bródy F., Vámos, T. (editors), ''The Neumann Compendium'', [[World Scientific]], p. 628; previously published in ''The Unity of Knowledge'', edited by L. Leary (1955), pp. 157-164, and also in ''John von Neumann Collected Works'', edited by A. Taub, Volume VI, pp. 491-498.</ref>
{{quote|text=... the sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work—that is, correctly to describe phenomena from a reasonably wide area.}}

There is also an increasing attention to scientific modelling<ref>Frigg and [[Stephan Hartmann|Hartmann]] (2009) state: "Philosophers are acknowledging the importance of models with increasing attention and are probing the assorted roles that models play in scientific practice". Source: Frigg, Roman and [[Stephan Hartmann|Hartmann, Stephan]], "Models in Science", ''The Stanford Encyclopedia of Philosophy'' (Summer 2009 Edition), Edward N. Zalta (ed.), ([http://plato.stanford.edu/archives/sum2009/entries/models-science/ source])</ref> in fields such as [[science education]],<ref>{{Cite journal|last1=Namdar|first1=Bahadir|last2=Shen|first2=Ji|date=2015-02-18|title=Modelling-Oriented Assessment in K-12 Science Education: A synthesis of research from 1980 to 2013 and new directions|journal=International Journal of Science Education|volume=37|issue=7|pages=993–1023|doi=10.1080/09500693.2015.1012185|bibcode=2015IJSEd..37..993N |s2cid=143865553|issn=0950-0693}}</ref> [[philosophy of science]], [[systems theory]], and [[Visualization (graphics)#Knowledge visualization|knowledge visualization]]. There is a growing collection of [[Scientific method|methods]], techniques and meta-[[theory]] about all kinds of specialized scientific modelling.

== Overview ==
[[File:MathModel.svg|right]]
A scientific model seeks to represent [[empiricism|empirical]] objects, phenomena, and physical processes in a [[logic]]al and [[Objectivity (philosophy)|objective]] way. All models are ''in simulacra'', that is, simplified reflections of reality that, despite being approximations, can be extremely useful.<ref>Box, George E.P. & Draper, N.R. (1987). [Empirical Model-Building and Response Surfaces.] ''Wiley''. p. 424</ref> Building and disputing models is fundamental to the scientific enterprise. Complete and true representation may be impossible, but scientific debate often concerns which is the better model for a given task, e.g., which is the more accurate climate model for seasonal forecasting.<ref>Hagedorn, R. ''et al.'' (2005) [http://www.ecmwf.int/staff/paco_doblas/abstr/tellus05_1.pdf, http://www.ecmwf.int/staff/paco_doblas/abstr/tellus05_1.pdf]{{dead link|date=May 2018 |bot=InternetArchiveBot |fix-attempted=yes }} ''Tellus'' 57A:219–33</ref>

Attempts to [[formal language|formalize]] the [[laws of science|principle]]s of the [[empirical science]]s use an [[interpretation (logic)|interpretation]] to model reality, in the same way logicians [[axiomatic system|axiomatize]] the [[rule of inference|principle]]s of [[logic]]. The aim of these attempts is to construct a [[formal system]] that will not produce theoretical consequences that are contrary to what is found in [[reality]]. Predictions or other statements drawn from such a formal system mirror or map the real world only insofar as these scientific models are true.<ref name="tcarotmimanass">[[Leo Apostel]] (1961). "Formal study of models". In: ''The Concept and the Role of the Model in Mathematics and Natural and Social''. Edited by [[Hans Freudenthal]]. Springer. pp. 8–9 ([https://books.google.com/books?id=8083fb2EuAMC&q=The+Concept+and+the+Role+of+the+Model+in+Mathematics+and+Natural+and+Social+Sciences&pg=PA8 Source])],</ref><ref>Ritchey, T.  (2012) [http://www.amg.swemorph.com/pdf/amg-1-1-2012.pdf Outline for a Morphology of Modelling Methods: Contribution to a General Theory of Modelling]</ref>

For the scientist, a model is also a way in which the human thought processes can be amplified.<ref>[[C. West Churchman]], ''The Systems Approach'', New York: Dell Publishing, 1968, p. 61</ref> For instance, 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. Such computer models are ''in silico''. Other types of scientific models are ''in vivo'' (living models, such as [[laboratory rat]]s) and ''in vitro'' (in glassware, such as [[tissue culture]]).<ref>Griffiths, E. C. (2010) [https://sites.google.com/a/ncsu.edu/emily-griffiths/whatisamodel.pdf What is a model?]</ref>

== Basics ==

===Modelling as a substitute for direct measurement and experimentation===
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 [[Scientific control|controlled conditions]] (see [[Scientific method]]) will always be more reliable than modeled estimates of outcomes.

Within [[modeling and simulation]], a model is a task-driven, purposeful simplification and abstraction of a perception of reality, shaped by physical, legal, and cognitive constraints.<ref>Tolk, A. (2015). Learning something right from models that are wrong – Epistemology of Simulation. In Yilmaz, L. (Ed.) ''Concepts and Methodologies in Modelling and Simulation.'' Springer–Verlag. pp. 87–106</ref> It is task-driven because a model is captured with a certain question or task in mind. Simplifications leave all the known and observed entities and their relation out that are not important for the task. Abstraction aggregates information that is important but not needed in the same detail as the object of interest. Both activities, simplification, and abstraction, are done purposefully. However, they are done based on a perception of reality. This perception is already a ''model'' in itself, as it comes with a physical constraint. There are also constraints on what we are able to legally observe with our current tools and methods, and cognitive constraints that limit what we are able to explain with our current theories. This model comprises the concepts, their behavior, and their relations informal form and is often referred to as a [[conceptual model]]. In order to execute the model, it needs to be implemented as a [[computer simulation]]. This requires more choices, such as numerical approximations or the use of heuristics.<ref>Oberkampf, W. L., DeLand, S. M., Rutherford, B. M., Diegert, K. V., & Alvin, K. F. (2002). Error and uncertainty in modelling and simulation. ''Reliability Engineering & System Safety'' 75(3): 333–57.</ref> Despite all these epistemological and computational constraints, simulation has been recognized as the third pillar of scientific methods: theory building, simulation, and experimentation.<ref>Ihrig, M. (2012). A New Research Architecture For The Simulation Era. In ''European Council on Modelling and Simulation''. pp. 715–20).</ref>

===Simulation===
A [[simulation]] is a way to implement the model, often employed when the model is too complex for the analytical solution. A steady-state simulation provides information about the system at a specific instant in time (usually at equilibrium, if such a state exists).  A dynamic simulation provides information over time. A simulation shows how a particular object or phenomenon will behave. Such a simulation can be useful for [[Experiment|testing]], analysis, or training in those cases where real-world systems or concepts can be represented by models.<ref name="SEF">[http://www.dau.mil/pubs/pdf/SEFGuide%2001-01.pdf ''Systems Engineering Fundamentals.''] {{webarchive|url=https://web.archive.org/web/20070927203501/http://www.dau.mil/pubs/pdf/SEFGuide%2001-01.pdf |date=2007-09-27 }} Defense Acquisition University Press, 2003.</ref>

===Structure===
[[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 field]]s, the concept of structure is an essential foundation of nearly every mode of inquiry and discovery in science, philosophy, and art.<ref name="Pullan000">{{cite book | last = Pullan | first = Wendy | title = Structure | publisher = Cambridge University Press | location = Cambridge | year = 2000 | isbn = 0-521-78258-9 }}</ref>

===Systems===
A [[system]] is a set of interacting or interdependent entities, real or abstract, forming an integrated whole. In general, a system is a construct or collection of different elements that together can produce results not obtainable by the elements alone.<ref>Fishwick PA. (1995). Simulation Model Design and Execution: Building Digital Worlds. Upper Saddle River, NJ: Prentice-Hall.</ref>  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 form relationships between an element of the set and elements not a part of the relational regime.  There are two types of system models: 1) discrete in which the variables change instantaneously at separate points in time and, 2) continuous where the state variables change continuously with respect to time.<ref>Sokolowski, J.A., Banks, C.M.(2009). Principles of Modelling and Simulation. Hoboken, NJ: John Wiley and Sons.</ref>

===Generating a model===
Modelling is the process of generating a model as a conceptual representation of some phenomenon. Typically a model will deal with only some aspects of the phenomenon in question, and two models of the same phenomenon may be essentially different—that is to say, that the differences between them comprise more than just a simple renaming of components.

Such differences may be due to differing requirements of the model's end users, or to conceptual or aesthetic differences among the modelers and to contingent decisions made during the modelling process. Considerations that may influence the [[structure]] of a model might be the modeler's preference for a reduced [[ontology]], preferences regarding [[statistical model]]s versus [[Deterministic system|deterministic models]], discrete versus continuous time, etc. In any case, users of a model need to understand the assumptions made that are pertinent to its validity for a given use.

Building a model requires [[abstraction]].  Assumptions are used in modelling in order to specify the domain of application of the model. For example, the [[Special relativity|special theory of relativity]] assumes an [[inertial frame of reference]]. This assumption was contextualized and further explained by the [[general theory of relativity]]. A model makes accurate predictions when its assumptions are valid, and might well not make accurate predictions when its assumptions do not hold. Such assumptions are often the point with which older theories are succeeded by new ones (the [[General relativity|general theory of relativity]] works in non-inertial reference frames as well).

===Evaluating a model===
{{See also|Models of scientific inquiry#Choice of a theory}}
A model is evaluated first and foremost by its consistency to empirical data; any model inconsistent with reproducible observations must be modified or rejected. One way to modify the model is by restricting the domain over which it is credited with having high validity. A case in point is Newtonian physics, which is highly useful except for the very small, the very fast, and the very massive phenomena of the universe. However, a fit to empirical data alone is not sufficient for a model to be accepted as valid.  Factors important in evaluating a model include:{{Citation needed|date=May 2008}}
* 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===
[[Visualization (computer graphics)|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 painting]]s, [[Egyptian hieroglyphs]], Greek [[geometry]], and [[Leonardo da Vinci]]'s revolutionary methods of technical drawing for engineering and scientific purposes.

===Space mapping===
[[Space mapping]] refers to a methodology that employs a "quasi-global" modelling formulation to link companion "coarse" (ideal or low-fidelity) with "fine" (practical or high-fidelity) models of different complexities. In [[engineering optimization]], space mapping aligns (maps) a very fast coarse model with its related expensive-to-compute fine model so as to avoid direct expensive optimization of the fine model. The alignment process iteratively refines a "mapped" coarse model ([[surrogate model]]).

== Types ==
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{{Col-break}}
* [[Analogical modeling|Analogical modelling]]
* [[Assembly modelling]]
* [[Catastrophe modeling|Catastrophe modelling]]
* [[Choice modelling]]
* [[Climate model]]
* [[Computational model]]
* [[Continuous modelling]]
* [[Data modeling|Data modelling]]
* [[Discrete modelling]]
* [[Document modelling]]
* [[Econometric model]]
* [[Economic model]]
* [[Ecosystem model]]
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* [[Empirical modelling]]
* [[Enterprise modelling]]
* [[Futures studies]]
* [[Geologic modelling]]
* [[Goal modeling]]
* [[Homology modeling|Homology modelling]]
* [[Hydrogeology]]
* [[Hydrography]]
* [[Hydrology#Hydrologic modeling|Hydrologic modelling]]
* [[Informative modelling]]
* [[Microscale and macroscale models|Macroscale modelling]]
* [[Mathematical model]]ling
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* [[Metabolic network modelling]]
* [[Microscale and macroscale models|Microscale modelling]]
* [[Modeling biological systems|Modelling biological systems]]
* [[Mathematical modelling of infectious disease|Modelling in epidemiology]]
* [[Molecular modelling]]
* Multicomputational model
* [[Multiscale modeling|Multiscale modelling]]
* [[Neuro-linguistic programming|NLP modelling]]
* [[Phenomenological model]]ling
* [[Predictive intake modelling]]
* [[Predictive modelling]]
* [[Scale model]]ling
* [[Simulation]]
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* [[Modeling language|Software modelling]]
* [[Solid modeling|Solid modelling]]
* [[Space mapping]]
* [[Statistical model]]
* [[Stochastic modelling (insurance)]]
* [[Surrogate model]]
* [[System architecture]]
* [[System dynamics]]
* [[Systems modeling|Systems modelling]]
* [[System-level_simulation|System-level modelling and simulation]]
* [[Water quality modelling]]
{{col-end}}

== Applications ==
===Modelling and simulation===

One application of scientific modelling is the field of [[modelling 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.
[[File:Modeling and Simulation Integrated Use.jpg|thumb|600px|center|Example of the integrated use of Modelling and Simulation in Defence life cycle management. The modelling and simulation in this image is represented in the center of the image with the three containers.<ref name="SEF"/>]]

The figure shows how modelling and simulation is used as a central part of an integrated program in a defence capability development process.<ref name="SEF"/>

== See also ==
* {{annotated link|Abductive reasoning}}
* {{annotated link|All models are wrong}}
* {{annotated link|Data and information visualization}}
* {{annotated link|Heuristic}}
* {{annotated link|Inverse problem}}
* {{annotated link|Scientific visualization}}
* {{annotated link|Statistical model}}

== References ==
{{reflist}}

== Further reading ==
Nowadays there are some 40 magazines about scientific modelling which offer all kinds of international forums. Since the 1960s there is a strongly growing number 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:
* Rainer Hegselmann, Ulrich Müller and Klaus Troitzsch (eds.) (1996). ''[https://books.google.com/books?id=y1dFny4vWt0C 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.
* Tom Ritchey (2012). "Outline for a Morphology of Modelling Methods:  Contribution to a General Theory of Modelling". In: ''Acta Morphologica Generalis'', Vol 1. No 1. pp.&nbsp;1–20.
* William Silvert (2001). "Modelling as a Discipline". In: ''Int. J. General Systems.'' Vol. 30(3), pp. 261.
* Sergio Sismondo and Snait Gissis (eds.) (1999). ''Modeling and Simulation. Special Issue of Science in Context'' 12.
* Eric Winsberg (2018) "Philosophy and Climate Science" Cambridge: [[Cambridge University Press]]
* Eric Winsberg (2010) "Science in the Age of Computer Simulation" Chicago: [[University of Chicago Press]]
* Eric Winsberg (2003). "Simulated Experiments: Methodology for a Virtual World". In: ''Philosophy of Science'' 70: 105–125.
* Tomáš Helikar, Jim A Rogers (2009). "[http://thecellcollective.org/cc.web/spring/internal-simulate?execution=e5s1 ChemChains]: a platform for simulation and analysis of biochemical networks aimed to laboratory scientists". [http://www.biomedcentral.com/1752-0509/3/58 BioMed Central].

== External links ==
{{wikiquote}}
{{Commonscat}}
*[http://www.iep.utm.edu/models/ Models]. Entry in the ''[[Internet Encyclopedia of Philosophy]]''
*[http://plato.stanford.edu/entries/models-science/ Models in Science]. Entry in the ''Stanford Encyclopedia of Philosophy''
*[http://philsci-archive.pitt.edu/archive/00002412/ 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.
*[https://web.archive.org/web/20121105182301/http://www.nsf.gov/cise/kdi/ideas/algorithms.html Research in simulation and modelling of various physical systems]
*[https://web.archive.org/web/20120314033220/http://wqic.nal.usda.gov/tools-and-guides/modeling Modelling] Water Quality Information Center, U.S. Department of Agriculture
*[http://www.ecotoxmodels.org/ Ecotoxicology & Models]
*[http://www.amg.swemorph.com/pdf/amg-1-1-2012.pdf/ A Morphology of Modelling Methods]. Acta Morphologica Generalis, Vol 1. No 1. pp.&nbsp;1–20.

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[[Category:Scientific modelling| ]]
[[Category:Conceptual modelling]]
[[Category:Epistemology of science]]
[[Category:Interpretation (philosophy)]]

[[it:Teoria#Modelli]]