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
''Visualize'' is a video release by Def Leppard. A compilation of promo videos, interviews, and concert footage. On DVD, it is bundled with '' Video Archive''. It won a 1993 Metal Edge Readers' Choice Award for "Best Home Video."Metal Edge, June ...
, or simulate by referencing it to existing and usually commonly accepted
knowledge
Knowledge can be defined as awareness of facts or as practical skills, and may also refer to familiarity with objects or situations. Knowledge of facts, also called propositional knowledge, is often defined as true belief that is disti ...
. 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 model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
s to quantify, computational models to simulate, and graphical models 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. The following was said by
John von Neumann
John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...
.
There is also an increasing attention to scientific modelling in fields such as
science education
Science education is the teaching and learning of science to school children, college students, or adults within the general public. The field of science education includes work in science content, science process (the scientific method), some ...
,
philosophy of science
Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ulti ...
theory
A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may ...
about all kinds of specialized scientific modelling.
Overview
A scientific model seeks to represent empirical objects, phenomena, and physical processes in a
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premis ...
al and objective way. All models are ''in simulacra'', that is, simplified reflections of reality that, despite being approximations, can be extremely useful. 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.
Attempts to formalize the principles of the empirical sciences use an
interpretation
Interpretation may refer to:
Culture
* Aesthetic interpretation, an explanation of the meaning of a work of art
* Allegorical interpretation, an approach that assumes a text should not be interpreted literally
* Dramatic Interpretation, an event ...
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premis ...
. 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.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 ]'',
For the scientist, a model is also a way in which the human thought processes can be amplified. 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).
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
The scientific method is an Empirical evidence, empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article hist ...
) 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. 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. Despite all these epistemological and computational constraints, simulation has been recognized as the third pillar of scientific methods: theory building, simulation, and experimentation.
Simulation
A
simulation
A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the ...
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.''Systems Engineering Fundamentals.'' Defense Acquisition University Press, 2003.
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
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...
s, the concept of structure is an essential foundation of nearly every mode of inquiry and discovery in science, philosophy, and art.
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. 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.Sokolowski, J.A., Banks, C.M.(2009). Principles of Modelling and Simulation. Hoboken, NJ: John Wiley and Sons.
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
In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality.
Ontology addresses questions like how entities are grouped into categories and which of these entities ...
, 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
Abstraction in its main sense is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or " concrete") signifiers, first principles, or other methods.
"An a ...
. Assumptions are used in modelling in order to specify the domain of application of the model. For example, the
special theory of relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
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
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:
* 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
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosoph ...
.
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 painting
In archaeology, Cave paintings are a type of parietal art (which category also includes petroglyphs, or engravings), found on the wall or ceilings of caves. The term usually implies prehistoric origin, and the oldest known are more than 40,00 ...
s,
Egyptian hieroglyphs
Egyptian hieroglyphs (, ) were the formal writing system used in Ancient Egypt, used for writing the Egyptian language. Hieroglyphs combined logographic, syllabic and alphabetic elements, with some 1,000 distinct characters.There were about 1, ...
, Greek
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, and
Leonardo da Vinci
Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, Drawing, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially re ...
'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 Engineering optimization
is the subject which uses optimization techniques to achieve design goals in engineering. It is sometimes referred to as design optimization.
Topics
* structural design (including pressure vessel design and welded bea ...
, 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).
Assembly modelling
Assembly modeling is a technology and method used by computer-aided design and product visualization computer software systems to handle multiple files that represent components within a product. The components within an assembly are represented a ...
*
Catastrophe modelling :''This article refers to the use of computers to estimate losses caused by disasters. For other meanings of the word catastrophe, including catastrophe theory in mathematics, see catastrophe (disambiguation).''
Catastrophe modeling (also known ...
*
Choice modelling Choice modelling attempts to model the decision process of an individual or segment via revealed preferences or stated preferences made in a particular context or contexts. Typically, it attempts to use discrete choices (A over B; B over A, B & C) ...
Discrete modelling Discrete modelling is the discrete analogue of continuous modelling
Continuous modelling is the mathematical practice of applying a model to continuous data (data which has a potentially infinite number, and divisibility, of attributes). They ofte ...
Futures studies
Futures studies, futures research, futurism or futurology is the systematic, interdisciplinary and holistic study of social and technological advancement, and other environmental trends, often for the purpose of exploring how people will l ...
Goal model
A goal is an idea of the future or desired result that a person or a group of people envision, plan and commit to achieve. People endeavour to reach goals within a finite time by setting deadlines.
A goal is roughly similar to a purpose or ai ...
Hydrogeology
Hydrogeology (''hydro-'' meaning water, and ''-geology'' meaning the study of the Earth) is the area of geology that deals with the distribution and movement of groundwater in the soil and rock (geology), rocks of the Earth's crust (ge ...
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
Predictive intake modelling Predictive intake modelling uses mathematical modelling strategies to estimate intake of food, personal care products, and their formulations.
Definition
Predictive intake modelling seeks to estimate intake of products and/or their constituents ...
Simulation
A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the ...
System dynamics
System dynamics (SD) is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays.
Overview
System dynamics is a methodology and mathematic ...
*
Systems modelling
Systems modeling or system modeling is the interdisciplinary study of the use of models to conceptualize and construct systems in business and IT development.System-level modelling and simulation
* Water quality modelling
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.
The figure shows how modelling and simulation is used as a central part of an integrated program in a defence capability development process.
See also
*
Abductive reasoning
Abductive reasoning (also called abduction,For example: abductive inference, or retroduction) is a form of logical inference formulated and advanced by American philosopher Charles Sanders Peirce beginning in the last third of the 19th centur ...
Heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediat ...
*
Inverse model
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the ...
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
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print book ...
.
* 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
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer.
Cambr ...
* Eric Winsberg (2010) "Science in the Age of Computer Simulation" Chicago:
University of Chicago Press
The University of Chicago Press is the largest and one of the oldest university presses in the United States. It is operated by the University of Chicago and publishes a wide variety of academic titles, including '' The Chicago Manual of Style'' ...
* 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
Internet Encyclopedia of Philosophy
The ''Internet Encyclopedia of Philosophy'' (''IEP'') is a scholarly online encyclopedia, dealing with philosophy, philosophical topics, and philosophers. The IEP combines open access publication with peer reviewed publication of original pa ...