Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to

understand Understanding is a psychological process related to an abstract or physical object, such as a person, situation, or message whereby one is able to use concepts to model that object. Understanding is a relation between the knower and an object of ...

define A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional defini ...

, quantify, visualize, 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 distin ...

. 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 A conceptual model is a representation of a system. It consists of concepts used to help people know, understand, or simulate a subject the model represents. In contrast, physical models are physical object such as a toy model that may be asse ...

s 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 A computational model uses computer programs to simulate and study complex systems using an algorithmic or mechanistic approach and is widely used in a diverse range of fields spanning from physics, chemistry and biology to economics, psychology, ...

to simulate, and

graphical model A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probabili ...

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. 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 c ...

. 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), som ...

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 ultim ...

systems theory Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structu ...

, and

knowledge visualization Visualization or visualisation (see spelling differences) 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 ...

. There is a growing collection of

methods Method ( grc, μέθοδος, methodos) literally means a pursuit of knowledge, investigation, mode of prosecuting such inquiry, or system. In recent centuries it more often means a prescribed process for completing a task. It may refer to: *Scien ...

, techniques and meta-

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 Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...

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 prem ...

al and

objective Objective may refer to: * Objective (optics), an element in a camera or microscope * ''The Objective'', a 2008 science fiction horror film * Objective pronoun, a personal pronoun that is used as a grammatical object * Objective Productions, a Brit ...

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

principle A principle is a proposition or value that is a guide for behavior or evaluation. In law, it is a rule that has to be or usually is to be followed. It can be desirably followed, or it can be an inevitable consequence of something, such as the l ...

s of the

empirical science In philosophy, empiricism is an epistemological theory that holds that knowledge or justification comes only or primarily from sensory experience. It is one of several views within epistemology, along with rationalism and skepticism. Empiri ...

s 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 ...

to model reality, in the same way logicians axiomatize the

s of

. The aim of these attempts is to construct a

formal system A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A fo ...

that will not produce theoretical consequences that are contrary to what is found in

reality Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that which is only imaginary. The term is also used to refer to the ontological status of things, indicating their existence. In physical terms, re ...

. 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 Leo Apostel (Antwerp, 4 September 1925 – Ghent, 10 August 1995) was a Belgian philosopher and professor at the Vrije Universiteit Brussel and Ghent University. Apostel was an advocate of interdisciplinary research and the bridging of the gap b ...

(1961). "Formal study of models". In: ''The Concept and the Role of the Model in Mathematics and Natural and Social''. Edited by

Hans Freudenthal Hans Freudenthal (17 September 1905 – 13 October 1990) was a Jewish-German-born Dutch mathematician. He made substantial contributions to algebraic topology and also took an interest in literature, philosophy, history and mathematics education ...

. 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 rat A laboratory rat or lab rat is a brown rat of the subspecies '' Rattus norvegicus domestica'' which is bred and kept for scientific research. While less commonly used for research than mice (see laboratory mouse), rats have served as an import ...

s) and ''in vitro'' (in glassware, such as

tissue culture Tissue culture is the growth of tissues or cells in an artificial medium separate from the parent organism. This technique is also called micropropagation. This is typically facilitated via use of a liquid, semi-solid, or solid growth medium, su ...

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 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 history of scientifi ...

) 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

. In order to execute the model, it needs to be implemented as a

computer simulation Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be deter ...

. 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

simulation A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of Conceptual model, models; the model represents the key characteristics or behaviors of the selected system or proc ...

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 An examination (exam or evaluation) or test is an educational assessment intended to measure a test-taker's knowledge, skill, aptitude, physical fitness, or classification in many other topics (e.g., beliefs). A test may be administered verba ...

, 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 A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such a ...

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 to ...

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

Systems

system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and express ...

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 A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such a ...

of a model might be the modeler's preference for a reduced

ontology In metaphysics, ontology is the philosophy, philosophical study of being, as well as related concepts such as existence, Becoming (philosophy), becoming, and reality. Ontology addresses questions like how entities are grouped into Category ...

, preferences regarding

statistical model A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form ...

s 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 abst ...

. 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 law ...

assumes an

inertial frame of reference In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. ...

. This assumption was contextualized and further explained by the

general theory of relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...

. 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

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 Visualization or visualisation may refer to: * Visualization (graphics), the physical or imagining creation of images, diagrams, or animations to communicate a message * Data visualization, the graphic representation of data * Information visuali ...

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 40,000 ye ...

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, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially rested on ...

'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 A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so a model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design ...

Types

* Analogical modelling *

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 ...

* Catastrophe modelling *

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) i ...

Climate model Numerical climate models use quantitative methods to simulate the interactions of the important drivers of climate, including atmosphere, oceans, land surface and ice. They are used for a variety of purposes from study of the dynamics of the c ...

Computational model A computational model uses computer programs to simulate and study complex systems using an algorithmic or mechanistic approach and is widely used in a diverse range of fields spanning from physics, chemistry and biology to economics, psychology, ...

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 often use differential equations and are converse to discrete modelling ...

Data modelling Data modeling in software engineering is the process of creating a data model for an information system by applying certain formal techniques. Overview Data modeling is a Software development process, process used to define and analyze dat ...

* Discrete modelling * Document modelling *

Econometric model Econometric models are statistical models used in econometrics. An econometric model specifies the statistical relationship that is believed to hold between the various economic quantities pertaining to a particular economic phenomenon. An econometr ...

Economic model In economics, a model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework desi ...

Ecosystem model An ecosystem model is an abstract, usually mathematical, representation of an ecological system (ranging in scale from an individual population, to an ecological community, or even an entire biome), which is studied to better understand the re ...

Empirical modelling Empirical modelling refers to any kind of (computer) modelling based on empirical observations rather than on mathematically describable relationships of the system modelled. Empirical Modelling Empirical Modelling as a variety of empirical mod ...

Enterprise modelling Enterprise modelling is the abstract representation, description and definition of the structure, processes, information and resources of an identifiable business, government body, or other large organization. It deals with the process of underst ...

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 ...

Geologic modelling Geologic modelling, geological modelling or geomodelling is the applied science of creating computerized representations of portions of the Earth's crust based on geophysical and geological observations made on and below the Earth surface. A ge ...

* Goal modelling * Homology modelling *

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 rocks of the Earth's crust (commonly in aq ...

Hydrography Hydrography is the branch of applied sciences which deals with the measurement and description of the physical features of oceans, seas, coastal areas, lakes and rivers, as well as with the prediction of their change over time, for the prima ...

* Hydrologic modelling * Informative modelling * Macroscale modelling *

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, ...

ling * Metabolic network modelling * Microscale modelling *

Modelling biological systems Modelling biological systems is a significant task of systems biology and mathematical biology. Computational systems biology aims to develop and use efficient algorithms, data structures, visualization and communication tools with the goal of comp ...

* Modelling in epidemiology *

Molecular modelling Molecular modelling encompasses all methods, theoretical and computational, used to model or mimic the behaviour of molecules. The methods are used in the fields of computational chemistry, drug design, computational biology and materials sci ...

* Multicomputational model * Multiscale modelling * NLP modelling *

Phenomenological model A phenomenological model is a scientific model that describes the empirical relationship of phenomena to each other, in a way which is consistent with fundamental theory, but is not directly derived from theory. In other words, a phenomenologica ...

ling * Predictive intake modelling *

Predictive modelling Predictive modelling uses statistics to predict outcomes. Most often the event one wants to predict is in the future, but predictive modelling can be applied to any type of unknown event, regardless of when it occurred. For example, predictive mod ...

Scale model A scale model is a physical model which is geometrically similar to an object (known as the prototype). Scale models are generally smaller than large prototypes such as vehicles, buildings, or people; but may be larger than small prototypes ...

ling *

Simulation A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of Conceptual model, models; the model represents the key characteristics or behaviors of the selected system or proc ...

* Software modelling *

Solid modelling Solid modeling (or solid modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes '' (solids)''. Solid modeling is distinguished from related areas of geometric modeling and computer graphi ...

* Space mapping *

Statistical model A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form ...

* Stochastic modelling (insurance) *

Surrogate model A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so a model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design ...

System architecture A system architecture is the conceptual model that defines the structure, behavior, and more views of a system. An architecture description is a formal description and representation of a system, organized in a way that supports reasoning about 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 mathematica ...

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 Water quality modeling involves water quality based data using mathematical simulation techniques. Water quality modeling helps people understand the eminence of water quality issues and models provide evidence for policy makers to make decisions ...

Applications

Modelling and simulation

One application of scientific modelling is the field of

modelling and simulation Modeling and simulation (M&S) is the use of Conceptual model, models (e.g., physical model, physical, mathematical, or logical data model, logical representation of a system, entity, phenomenon, or process) as a basis for simulations to develop da ...

, 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. Modeling and Simulation Integrated Use

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

References

External links

Models
Entry in the ''

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 p ...

''
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.

* ttp://wqic.nal.usda.gov/tools-and-guides/modeling ModellingWater Quality Information Center, U.S. Department of Agriculture
Ecotoxicology & ModelsA Morphology of Modelling Methods
Acta Morphologica Generalis, Vol 1. No 1. pp. 1–20. {{DEFAULTSORT:Scientific Modelling Conceptual modelling Epistemology of science Interpretation (philosophy) it:Teoria#Modelli