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Scientific modelling

January 20, 2023

Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. 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 models to better understand, operational models to operationalize, mathematical models to quantify, computational models to simulate, and graphical models to visualize the subject.

Example scientific modelling. A schematic of chemical and transport processes related to atmospheric composition.

Modelling is an essential and inseparable part of many scientific disciplines, each of which has its own ideas about specific types of modelling.[1][2] The following was said by John von Neumann.[3]

... 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[4] in fields such as science education,[5] philosophy of science, systems theory, and knowledge visualization. There is a growing collection of methods, techniques and meta-theory about all kinds of specialized scientific modelling.

Overview

 

A scientific model seeks to represent empirical objects, phenomena, and physical processes in a logical and objective way. All models are in simulacra, that is, simplified reflections of reality that, despite being approximations, can be extremely useful.[6] 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.[7]

Attempts to formalize the principles of the empirical sciences use an interpretation to model reality, in the same way logicians axiomatize the principles 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.[8][9]

For the scientist, a model is also a way in which the human thought processes can be amplified.[10] 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 rats) and in vitro (in glassware, such as tissue culture).[11]

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 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.[12] 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.[13] Despite all these epistemological and computational constraints, simulation has been recognized as the third pillar of scientific methods: theory building, simulation, and experimentation.[14]

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 testing, analysis, or training in those cases where real-world systems or concepts can be represented by models.[15]

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 fields, the concept of structure is an essential foundation of nearly every mode of inquiry and discovery in science, philosophy, and art.[16]

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.[17] 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.[18]

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 models versus 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 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 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]

  • 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 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.

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

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.

 
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.[15]

The figure shows how modelling and simulation is used as a central part of an integrated program in a defence capability development process.[15]

See also

References

  1. ^ Cartwright, Nancy. 1983. How the Laws of Physics Lie. Oxford University Press
  2. ^ Hacking, Ian. 1983. Representing and Intervening. Introductory Topics in the Philosophy of Natural Science. Cambridge University Press
  3. ^ 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.
  4. ^ Frigg and 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 Hartmann, Stephan, "Models in Science", The Stanford Encyclopedia of Philosophy (Summer 2009 Edition), Edward N. Zalta (ed.), (source)
  5. ^ Namdar, Bahadir; Shen, Ji (2015-02-18). "Modelling-Oriented Assessment in K-12 Science Education: A synthesis of research from 1980 to 2013 and new directions". International Journal of Science Education. 37 (7): 993–1023. Bibcode:2015IJSEd..37..993N. doi:10.1080/09500693.2015.1012185. ISSN 0950-0693. S2CID 143865553.
  6. ^ Box, George E.P. & Draper, N.R. (1987). [Empirical Model-Building and Response Surfaces.] Wiley. p. 424
  7. ^ Hagedorn, R. et al. (2005) http://www.ecmwf.int/staff/paco_doblas/abstr/tellus05_1.pdf[permanent dead link] Tellus 57A:219–33
  8. ^ 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 (Source)],
  9. ^ Ritchey, T. (2012) Outline for a Morphology of Modelling Methods: Contribution to a General Theory of Modelling
  10. ^ C. West Churchman, The Systems Approach, New York: Dell Publishing, 1968, p. 61
  11. ^ Griffiths, E. C. (2010) What is a model?
  12. ^ 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
  13. ^ 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.
  14. ^ Ihrig, M. (2012). A New Research Architecture For The Simulation Era. In European Council on Modelling and Simulation. pp. 715–20).
  15. ^ a b c Systems Engineering Fundamentals. 2007-09-27 at the Wayback Machine Defense Acquisition University Press, 2003.
  16. ^ Pullan, Wendy (2000). Structure. Cambridge: Cambridge University Press. ISBN 0-521-78258-9.
  17. ^ Fishwick PA. (1995). Simulation Model Design and Execution: Building Digital Worlds. Upper Saddle River, NJ: Prentice-Hall.
  18. ^ Sokolowski, J.A., Banks, C.M.(2009). Principles of Modelling and Simulation. Hoboken, NJ: John Wiley and Sons.

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). 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. 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). "ChemChains: a platform for simulation and analysis of biochemical networks aimed to laboratory scientists". BioMed Central.

External links

 
Wikiquote has quotations related to Scientific modelling.
 
Wikimedia Commons has media related to Scientific modeling.
  • Models. Entry in the Internet Encyclopedia of Philosophy
  • 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.
  • Modelling Water Quality Information Center, U.S. Department of Agriculture
  • Ecotoxicology & Models
  • A Morphology of Modelling Methods. Acta Morphologica Generalis, Vol 1. No 1. pp. 1–20.

January 20, 2023
scientific, modelling, scientific, activity, which, make, particular, part, feature, world, easier, understand, define, quantify, visualize, simulate, referencing, existing, usually, commonly, accepted, knowledge, requires, selecting, identifying, relevant, as. Scientific modelling is a scientific activity the aim of which is to make a particular part or feature of the world easier to understand define quantify visualize or simulate by referencing it to existing and usually commonly accepted knowledge 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 models to better understand operational models to operationalize mathematical models to quantify computational models to simulate and graphical models to visualize the subject Example scientific modelling A schematic of chemical and transport processes related to atmospheric composition Modelling is an essential and inseparable part of many scientific disciplines each of which has its own ideas about specific types of modelling 1 2 The following was said by John von Neumann 3 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 4 in fields such as science education 5 philosophy of science systems theory and knowledge visualization There is a growing collection of methods techniques and meta theory about all kinds of specialized scientific modelling Contents 1 Overview 2 Basics 2 1 Modelling as a substitute for direct measurement and experimentation 2 2 Simulation 2 3 Structure 2 4 Systems 2 5 Generating a model 2 6 Evaluating a model 2 7 Visualization 2 8 Space mapping 3 Types 4 Applications 4 1 Modelling and simulation 5 See also 6 References 7 Further reading 8 External linksOverview Edit A scientific model seeks to represent empirical objects phenomena and physical processes in a logical and objective way All models are in simulacra that is simplified reflections of reality that despite being approximations can be extremely useful 6 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 7 Attempts to formalize the principles of the empirical sciences use an interpretation to model reality in the same way logicians axiomatize the principles 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 8 9 For the scientist a model is also a way in which the human thought processes can be amplified 10 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 rats and in vitro in glassware such as tissue culture 11 Basics EditModelling as a substitute for direct measurement and experimentation Edit 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 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 12 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 13 Despite all these epistemological and computational constraints simulation has been recognized as the third pillar of scientific methods theory building simulation and experimentation 14 Simulation Edit 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 testing analysis or training in those cases where real world systems or concepts can be represented by models 15 Structure Edit 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 16 Systems Edit 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 17 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 18 Generating a model Edit 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 models versus 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 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 theory of relativity works in non inertial reference frames as well Evaluating a model Edit 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 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 appealPeople may attempt to quantify the evaluation of a model using a utility function Visualization Edit 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 Space mapping Edit 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 EditAnalogical modelling Assembly modelling Catastrophe modelling Choice modelling Climate model Computational model Continuous modelling Data modelling Discrete modelling Document modelling Econometric model Economic model Ecosystem model Empirical modelling Enterprise modelling Futures studies Geologic modelling Goal modelling Homology modelling Hydrogeology Hydrography Hydrologic modelling Informative modelling Macroscale modelling Mathematical modelling Metabolic network modelling Microscale modelling Modelling biological systems Modelling in epidemiology Molecular modelling Multicomputational model Multiscale modelling NLP modelling Phenomenological modelling Predictive intake modelling Predictive modelling Scale modelling Simulation Software modelling Solid modelling Space mapping Statistical model Stochastic modelling insurance Surrogate model System architecture System dynamics Systems modelling System level modelling and simulation Water quality modellingApplications EditModelling and simulation Edit One application of scientific modelling is the field of modelling and simulation generally referred to as M amp S M amp 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 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 15 The figure shows how modelling and simulation is used as a central part of an integrated program in a defence capability development process 15 See also EditAbductive reasoning All models are wrong Heuristic Inverse model Scientific visualization Statistical modelReferences Edit Cartwright Nancy 1983 How the Laws of Physics Lie Oxford University Press Hacking Ian 1983 Representing and Intervening Introductory Topics in the Philosophy of Natural Science Cambridge University Press von Neumann J 1995 Method in the physical sciences in Brody F Vamos 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 Frigg and 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 Hartmann Stephan Models in Science The Stanford Encyclopedia of Philosophy Summer 2009 Edition Edward N Zalta ed source Namdar Bahadir Shen Ji 2015 02 18 Modelling Oriented Assessment in K 12 Science Education A synthesis of research from 1980 to 2013 and new directions International Journal of Science Education 37 7 993 1023 Bibcode 2015IJSEd 37 993N doi 10 1080 09500693 2015 1012185 ISSN 0950 0693 S2CID 143865553 Box George E P amp Draper N R 1987 Empirical Model Building and Response Surfaces Wiley p 424 Hagedorn R et al 2005 http www ecmwf int staff paco doblas abstr tellus05 1 pdf permanent dead link Tellus 57A 219 33 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 Source Ritchey T 2012 Outline for a Morphology of Modelling Methods Contribution to a General Theory of Modelling C West Churchman The Systems Approach New York Dell Publishing 1968 p 61 Griffiths E C 2010 What is a model 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 Oberkampf W L DeLand S M Rutherford B M Diegert K V amp Alvin K F 2002 Error and uncertainty in modelling and simulation Reliability Engineering amp System Safety 75 3 333 57 Ihrig M 2012 A New Research Architecture For The Simulation Era In European Council on Modelling and Simulation pp 715 20 a b c Systems Engineering Fundamentals Archived 2007 09 27 at the Wayback Machine Defense Acquisition University Press 2003 Pullan Wendy 2000 Structure Cambridge Cambridge University Press ISBN 0 521 78258 9 Fishwick PA 1995 Simulation Model Design and Execution Building Digital Worlds Upper Saddle River NJ Prentice Hall Sokolowski J A Banks C M 2009 Principles of Modelling and Simulation Hoboken NJ John Wiley and Sons Further reading EditNowadays 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 Muller 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 Gunter Kuppers 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 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 Tomas Helikar Jim A Rogers 2009 ChemChains a platform for simulation and analysis of biochemical networks aimed to laboratory scientists BioMed Central External links Edit Wikiquote has quotations related to Scientific modelling Wikimedia Commons has media related to Scientific modeling Models Entry in the Internet Encyclopedia of Philosophy 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 modelling of various physical systems Modelling Water Quality Information Center U S Department of Agriculture Ecotoxicology amp Models A Morphology of Modelling Methods Acta Morphologica Generalis Vol 1 No 1 pp 1 20 Retrieved from https en wikipedia org w index php title Scientific modelling amp oldid 1125303409, wikipedia, wiki, book, books, library,

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