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Computer simulation is the running of a
mathematical model A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...
on a
computer A computer is a machine that can be Computer programming, programmed to automatically Execution (computing), carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic set ...
, the
model A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , . Models can be divided in ...
being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer
simulation A simulation is an imitative representation of a process or system that could exist in the real world. In this broad sense, simulation can often be used interchangeably with model. Sometimes a clear distinction between the two terms is made, in ...
s have become a useful tool for the mathematical modeling of many natural systems in
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
(
computational physics Computational physics is the study and implementation of numerical analysis to solve problems in physics. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science ...
),
astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the ...
,
climatology Climatology (from Greek , ''klima'', "slope"; and , '' -logia'') or climate science is the scientific study of Earth's climate, typically defined as weather conditions averaged over a period of at least 30 years. Climate concerns the atmospher ...
,
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
,
biology Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...
and
manufacturing Manufacturing is the creation or production of goods with the help of equipment, labor, machines, tools, and chemical or biological processing or formulation. It is the essence of the secondary sector of the economy. The term may refer ...
, as well as human systems in
economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...
,
psychology Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ...
,
social science Social science (often rendered in the plural as the social sciences) is one of the branches of science, devoted to the study of societies and the relationships among members within those societies. The term was formerly used to refer to the ...
,
health care Health care, or healthcare, is the improvement or maintenance of health via the preventive healthcare, prevention, diagnosis, therapy, treatment, wikt:amelioration, amelioration or cure of disease, illness, injury, and other disability, physic ...
and
engineering Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...
. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new
technology Technology is the application of Conceptual model, conceptual knowledge to achieve practical goals, especially in a reproducible way. The word ''technology'' can also mean the products resulting from such efforts, including both tangible too ...
and to estimate the performance of systems too complex for
analytical solution In mathematics, an expression or equation is in closed form if it is formed with constants, variables, and a set of functions considered as ''basic'' and connected by arithmetic operations (, and integer powers) and function composition. C ...
s. Computer simulations are realized by running
computer program A computer program is a sequence or set of instructions in a programming language for a computer to Execution (computing), execute. It is one component of software, which also includes software documentation, documentation and other intangibl ...
s that can be either small, running almost instantly on small devices, or large-scale programs that run for hours or days on network-based groups of computers. The scale of events being simulated by computer simulations has far exceeded anything possible (or perhaps even imaginable) using traditional paper-and-pencil mathematical modeling. In 1997, a desert-battle simulation of one force invading another involved the modeling of 66,239 tanks, trucks and other vehicles on simulated terrain around
Kuwait Kuwait, officially the State of Kuwait, is a country in West Asia and the geopolitical region known as the Middle East. It is situated in the northern edge of the Arabian Peninsula at the head of the Persian Gulf, bordering Iraq to Iraq–Kuwait ...
, using multiple supercomputers in the DoD High Performance Computer Modernization Program. Other examples include a 1-billion-atom model of material deformation; a 2.64-million-atom model of the complex protein-producing organelle of all living organisms, the
ribosome Ribosomes () are molecular machine, macromolecular machines, found within all cell (biology), cells, that perform Translation (biology), biological protein synthesis (messenger RNA translation). Ribosomes link amino acids together in the order s ...
, in 2005; a complete simulation of the life cycle of ''
Mycoplasma genitalium ''Mycoplasma genitalium'' (also known as ''MG','' Mgen, or since 2018, ''Mycoplasmoides genitalium'') is a sexually transmitted, small and pathogenic bacterium that lives on the mucous epithelial cells of the urinary and genital tracts in ...
'' in 2012; and the
Blue Brain The Blue Brain Project was a Swiss brain research initiative that aimed to create a Artificial brain, digital reconstruction of the mouse brain. The project was founded in May 2005 by the Brain Mind Institute of ''École Polytechnique Fédérale de ...
project at EPFL (Switzerland), begun in May 2005 to create the first computer simulation of the entire human brain, right down to the molecular level. Because of the computational cost of simulation,
computer experiment A computer experiment or simulation experiment is an experiment used to study a computer simulation, also referred to as an in silico system. This area includes computational physics, computational chemistry, computational biology and other simila ...
s are used to perform inference such as
uncertainty quantification Uncertainty quantification (UQ) is the science of quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system ...
.


Simulation versus model

A model consists of the equations used to capture the behavior of a system. By contrast, computer simulation is the actual running of the program that perform algorithms which solve those equations, often in an approximate manner. Simulation, therefore, is the process of running a model. Thus one would not "build a simulation"; instead, one would "build a model (or a simulator)", and then either "run the model" or equivalently "run a simulation".


History

Computer simulation developed hand-in-hand with the rapid growth of the computer, following its first large-scale deployment during the
Manhattan Project The Manhattan Project was a research and development program undertaken during World War II to produce the first nuclear weapons. It was led by the United States in collaboration with the United Kingdom and Canada. From 1942 to 1946, the ...
in
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
to model the process of nuclear detonation. It was a simulation of 12 hard spheres using a
Monte Carlo algorithm In computing, a Monte Carlo algorithm is a randomized algorithm whose output may be incorrect with a certain (typically small) probability. Two examples of such algorithms are the Karger–Stein algorithm and the Monte Carlo algorithm for mini ...
. Computer simulation is often used as an adjunct to, or substitute for, modeling systems for which simple closed form analytic solutions are not possible. There are many types of computer simulations; their common feature is the attempt to generate a sample of representative scenarios for a model in which a complete enumeration of all possible states of the model would be prohibitive or impossible.


Data preparation

The external data requirements of simulations and models vary widely. For some, the input might be just a few numbers (for example, simulation of a waveform of AC electricity on a wire), while others might require terabytes of information (such as weather and climate models). Input sources also vary widely: * Sensors and other physical devices connected to the model; * Control surfaces used to direct the progress of the simulation in some way; * Current or historical data entered by hand; * Values extracted as a by-product from other processes; * Values output for the purpose by other simulations, models, or processes. Lastly, the time at which data is available varies: * "invariant" data is often built into the model code, either because the value is truly invariant (e.g., the value of π) or because the designers consider the value to be invariant for all cases of interest; * data can be entered into the simulation when it starts up, for example by reading one or more files, or by reading data from a
preprocessor In computer science, a preprocessor (or precompiler) is a Computer program, program that processes its input data to produce output that is used as input in another program. The output is said to be a preprocessed form of the input data, which i ...
; * data can be provided during the simulation run, for example by a sensor network. Because of this variety, and because diverse simulation systems have many common elements, there are a large number of specialized simulation languages. The best-known may be
Simula Simula is the name of two simulation programming languages, Simula I and Simula 67, developed in the 1960s at the Norwegian Computing Center in Oslo, by Ole-Johan Dahl and Kristen Nygaard. Syntactically, it is an approximate superset of AL ...
. There are now many others. Systems that accept data from external sources must be very careful in knowing what they are receiving. While it is easy for computers to read in values from text or binary files, what is much harder is knowing what the
accuracy Accuracy and precision are two measures of ''observational error''. ''Accuracy'' is how close a given set of measurements (observations or readings) are to their ''true value''. ''Precision'' is how close the measurements are to each other. The ...
(compared to
measurement resolution A sensor is often defined as a device that receives and responds to a signal or stimulus. The stimulus is the quantity, property, or condition that is sensed and converted into electrical signal. In the broadest definition, a sensor is a devi ...
and precision) of the values are. Often they are expressed as "error bars", a minimum and maximum deviation from the value range within which the true value (is expected to) lie. Because digital computer mathematics is not perfect, rounding and truncation errors multiply this error, so it is useful to perform an "error analysis" to confirm that values output by the simulation will still be usefully accurate.


Types

Models used for computer simulations can be classified according to several independent pairs of attributes, including: *
Stochastic Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; i ...
or
deterministic Determinism is the metaphysical view that all events within the universe (or multiverse) can occur only in one possible way. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping mo ...
(and as a special case of deterministic, chaotic) – see external links below for examples of stochastic vs. deterministic simulations * Steady-state or dynamic * Continuous or
discrete Discrete may refer to: *Discrete particle or quantum in physics, for example in quantum theory * Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit * Discrete group, ...
(and as an important special case of discrete, discrete event or DE models) * Dynamic system simulation, e.g. electric systems, hydraulic systems or multi-body mechanical systems (described primarily by DAE:s) or dynamics simulation of field problems, e.g. CFD of FEM simulations (described by PDE:s). * Local or distributed. Another way of categorizing models is to look at the underlying data structures. For time-stepped simulations, there are two main classes: * Simulations which store their data in regular grids and require only next-neighbor access are called stencil codes. Many CFD applications belong to this category. * If the underlying graph is not a regular grid, the model may belong to the meshfree method class. For steady-state simulations, equations define the relationships between elements of the modeled system and attempt to find a state in which the system is in equilibrium. Such models are often used in simulating physical systems, as a simpler modeling case before dynamic simulation is attempted. * Dynamic simulations attempt to capture changes in a system in response to (usually changing) input signals. * ''
Stochastic Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; i ...
'' models use ''
random number generator Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that cannot be reasonably predicted better than by random chance. This means that the particular ou ...
s'' to model chance or random events; * A ''
discrete event simulation A discrete-event simulation (DES) models the operation of a system as a (discrete) sequence of events in time. Each event occurs at a particular instant in time and marks a change of state in the system. Between consecutive events, no change in th ...
'' (DES) manages events in time. Most computer, logic-test and fault-tree simulations are of this type. In this type of simulation, the simulator maintains a queue of events sorted by the simulated time they should occur. The simulator reads the queue and triggers new events as each event is processed. It is not important to execute the simulation in real time. It is often more important to be able to access the data produced by the simulation and to discover logic defects in the design or the sequence of events. * A ''continuous dynamic simulation'' performs numerical solution of differential-algebraic equations or differential equations (either
partial Partial may refer to: Mathematics *Partial derivative, derivative with respect to one of several variables of a function, with the other variables held constant ** ∂, a symbol that can denote a partial derivative, sometimes pronounced "partial d ...
or ordinary). Periodically, the simulation program solves all the equations and uses the numbers to change the state and output of the simulation. Applications include flight simulators, construction and management simulation games, chemical process modeling, and simulations of
electrical circuit An electrical network is an interconnection of electrical components (e.g., battery (electricity), batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e. ...
s. Originally, these kinds of simulations were actually implemented on
analog computer An analog computer or analogue computer is a type of computation machine (computer) that uses physical phenomena such as Electrical network, electrical, Mechanics, mechanical, or Hydraulics, hydraulic quantities behaving according to the math ...
s, where the differential equations could be represented directly by various electrical components such as op-amps. By the late 1980s, however, most "analog" simulations were run on conventional
digital computer A computer is a machine that can be programmed to automatically carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic sets of operations known as ''programs'', wh ...
s that emulate the behavior of an analog computer. * A special type of discrete simulation that does not rely on a model with an underlying equation, but can nonetheless be represented formally, is agent-based simulation. In agent-based simulation, the individual entities (such as molecules, cells, trees or consumers) in the model are represented directly (rather than by their density or concentration) and possess an internal state and set of behaviors or rules that determine how the agent's state is updated from one time-step to the next. * Distributed models run on a network of interconnected computers, possibly through the
Internet The Internet (or internet) is the Global network, global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a internetworking, network of networks ...
. Simulations dispersed across multiple host computers like this are often referred to as "distributed simulations". There are several standards for distributed simulation, including Aggregate Level Simulation Protocol (ALSP),
Distributed Interactive Simulation Distributed Interactive Simulation (DIS) is an IEEE standard for conducting real-time platform-level wargaming across multiple host computers and is used worldwide, especially by military organizations but also by other agencies such as those inv ...
(DIS), the High Level Architecture (simulation) (HLA) and the Test and Training Enabling Architecture (TENA).


Visualization

Formerly, the output data from a computer simulation was sometimes presented in a table or a matrix showing how data were affected by numerous changes in the simulation parameters. The use of the matrix format was related to traditional use of the matrix concept in
mathematical model A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...
s. However, psychologists and others noted that humans could quickly perceive trends by looking at graphs or even moving-images or motion-pictures generated from the data, as displayed by computer-generated-imagery (CGI) animation. Although observers could not necessarily read out numbers or quote math formulas, from observing a moving weather chart they might be able to predict events (and "see that rain was headed their way") much faster than by scanning tables of rain-cloud
coordinate In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...
s. Such intense graphical displays, which transcended the world of numbers and formulae, sometimes also led to output that lacked a coordinate grid or omitted timestamps, as if straying too far from numeric data displays. Today,
weather forecasting Weather forecasting or weather prediction is the application of science and technology forecasting, to predict the conditions of the Earth's atmosphere, atmosphere for a given location and time. People have attempted to predict the weather info ...
models tend to balance the view of moving rain/snow clouds against a map that uses numeric coordinates and numeric timestamps of events. Similarly, CGI computer simulations of CAT scans can simulate how a
tumor A neoplasm () is a type of abnormal and excessive growth of tissue. The process that occurs to form or produce a neoplasm is called neoplasia. The growth of a neoplasm is uncoordinated with that of the normal surrounding tissue, and persists ...
might shrink or change during an extended period of medical treatment, presenting the passage of time as a spinning view of the visible human head, as the tumor changes. Other applications of CGI computer simulations are being developed to graphically display large amounts of data, in motion, as changes occur during a simulation run.


In science

Generic examples of types of computer simulations in science, which are derived from an underlying mathematical description: * a numerical simulation of differential equations that cannot be solved analytically, theories that involve continuous systems such as phenomena in
physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fu ...
,
fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...
(e.g.,
climate model Numerical climate models (or climate system models) are mathematical models that can simulate the interactions of important drivers of climate. These drivers are the atmosphere, oceans, land surface and ice. Scientists use climate models to st ...
s, roadway noise models, roadway air dispersion models),
continuum mechanics Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a ''continuous medium'' (also called a ''continuum'') rather than as discrete particles. Continuum mec ...
and
chemical kinetics Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is different from chemical thermodynamics, which deals with the direction in which a ...
fall into this category. * a
stochastic Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; i ...
simulation, typically used for discrete systems where events occur
probabilistic Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
ally and which cannot be described directly with differential equations (this is a ''discrete'' simulation in the above sense). Phenomena in this category include
genetic drift Genetic drift, also known as random genetic drift, allelic drift or the Wright effect, is the change in the Allele frequency, frequency of an existing gene variant (allele) in a population due to random chance. Genetic drift may cause gene va ...
,
biochemical Biochemistry, or biological chemistry, is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology, ...
or
gene regulatory network A gene (or genetic) regulatory network (GRN) is a collection of molecular regulators that interact with each other and with other substances in the cell to govern the gene expression levels of mRNA and proteins which, in turn, determine the fu ...
s with small numbers of molecules. (see also:
Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be ...
). * multiparticle simulation of the response of nanomaterials at multiple scales to an applied force for the purpose of modeling their thermoelastic and thermodynamic properties. Techniques used for such simulations are
Molecular dynamics Molecular dynamics (MD) is a computer simulation method for analyzing the Motion (physics), physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamics ( ...
,
Molecular mechanics Molecular mechanics uses classical mechanics to model molecular systems. The Born–Oppenheimer approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using Force field (chemi ...
,
Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be ...
, and Multiscale Green's function. Specific examples of computer simulations include: * statistical simulations based upon an agglomeration of a large number of input profiles, such as the forecasting of equilibrium
temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
of receiving waters, allowing the gamut of
meteorological Meteorology is the scientific study of the Earth's atmosphere and short-term atmospheric phenomena (i.e. weather), with a focus on weather forecasting. It has applications in the military, aviation, energy production, transport, agriculture ...
data to be input for a specific locale. This technique was developed for
thermal pollution Thermal pollution, sometimes called "thermal enrichment", is the degradation of water quality by any process that changes ambient water temperature. Thermal pollution is the rise or drop in the temperature of a natural body of water caused by h ...
forecasting. * agent based simulation has been used effectively in
ecology Ecology () is the natural science of the relationships among living organisms and their Natural environment, environment. Ecology considers organisms at the individual, population, community (ecology), community, ecosystem, and biosphere lev ...
, where it is often called "individual based modeling" and is used in situations for which individual variability in the agents cannot be neglected, such as
population dynamics Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. Population dynamics is a branch of mathematical biology, and uses mathematical techniques such as differenti ...
of
salmon Salmon (; : salmon) are any of several list of commercially important fish species, commercially important species of euryhaline ray-finned fish from the genera ''Salmo'' and ''Oncorhynchus'' of the family (biology), family Salmonidae, native ...
and
trout Trout (: trout) is a generic common name for numerous species of carnivorous freshwater ray-finned fishes belonging to the genera '' Oncorhynchus'', ''Salmo'' and ''Salvelinus'', all of which are members of the subfamily Salmoninae in the ...
(most purely mathematical models assume all trout behave identically). * time stepped dynamic model. In hydrology there are several such hydrology transport models such as the
SWMM The United States Environmental Protection Agency (EPA) Storm Water Management Model (SWMM) is a dynamic rainfall–surface runoff, runoff–groundwater, subsurface runoff Scientific modelling, simulation model used for single-event to long-term ( ...
and
DSSAM Model The DSSAM Model (Dynamic Stream Simulation and Assessment Model) is a computer simulation developed for the Truckee River to analyze water pollution, water quality impacts from land use and wastewater management decisions in the Truckee River Bas ...
s developed by the U.S. Environmental Protection Agency for river water quality forecasting. * computer simulations have also been used to formally model theories of human cognition and performance, e.g.,
ACT-R ACT-R (pronounced /ˌækt ˈɑr/; short for "Adaptive Control of Thought—Rational") is a cognitive architecture mainly developed by John Robert Anderson and Christian Lebiere at Carnegie Mellon University. Like any cognitive architecture, ACT ...
. * computer simulation using molecular modeling for
drug discovery In the fields of medicine, biotechnology, and pharmacology, drug discovery is the process by which new candidate medications are discovered. Historically, drugs were discovered by identifying the active ingredient from traditional remedies or ...
. * computer simulation to model viral infection in mammalian cells. * computer simulation for studying the selective sensitivity of bonds by mechanochemistry during grinding of organic molecules. *
Computational fluid dynamics Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid dynamics, fluid flows. Computers are used to perform the calculations required ...
simulations are used to simulate the behaviour of flowing air, water and other fluids. One-, two- and three-dimensional models are used. A one-dimensional model might simulate the effects of
water hammer Hydraulic shock ( colloquial: water hammer; fluid hammer) is a pressure surge or wave caused when a fluid in motion is forced to stop or change direction suddenly: a momentum change. It is usually observed in a liquid but gases can also be aff ...
in a pipe. A two-dimensional model might be used to simulate the drag forces on the cross-section of an aeroplane wing. A three-dimensional simulation might estimate the heating and cooling requirements of a large building. * An understanding of statistical thermodynamic molecular theory is fundamental to the appreciation of molecular solutions. Development of the Potential Distribution Theorem (PDT) allows this complex subject to be simplified to down-to-earth presentations of molecular theory. Notable, and sometimes controversial, computer simulations used in science include:
Donella Meadows Donella Hager "Dana" Meadows (March 13, 1941 – February 20, 2001) was an American environmental scientist, educator, and writer. She is best known as lead author of the books '' The Limits to Growth'' and '' Thinking In Systems: A Primer''. ...
' World3 used in the '' Limits to Growth'', James Lovelock's Daisyworld and Thomas Ray's Tierra. In social sciences, computer simulation is an integral component of the five angles of analysis fostered by the data percolation methodology, which also includes qualitative and quantitative methods, reviews of the literature (including scholarly), and interviews with experts, and which forms an extension of data triangulation. Of course, similar to any other scientific method, replication is an important part of computational modeling


In practical contexts

Computer simulations are used in a wide variety of practical contexts, such as: * analysis of
air pollutant Air pollution is the presence of substances in the air that are harmful to humans, other living beings or the environment. Pollutants can be gases like ozone or nitrogen oxides or small particles like soot and dust. It affects both outdoor ...
dispersion using atmospheric dispersion modeling * As a possible humane alternative to live
animal testing Animal testing, also known as animal experimentation, animal research, and ''in vivo'' testing, is the use of animals, as model organisms, in experiments that seek answers to scientific and medical questions. This approach can be contrasted ...
in respect to
animal rights Animal rights is the philosophy according to which many or all Animal consciousness, sentient animals have Moral patienthood, moral worth independent of their Utilitarianism, utility to humans, and that their most basic interests—such as ...
. * design of complex systems such as
aircraft An aircraft ( aircraft) is a vehicle that is able to flight, fly by gaining support from the Atmosphere of Earth, air. It counters the force of gravity by using either Buoyancy, static lift or the Lift (force), dynamic lift of an airfoil, or, i ...
and also
logistics Logistics is the part of supply chain management that deals with the efficient forward and reverse flow of goods, services, and related information from the point of origin to the Consumption (economics), point of consumption according to the ...
systems. * design of
noise barrier A noise barrier (also called a soundwall, noise wall, sound berm, sound barrier, or acoustical barrier) is an exterior structure designed to protect inhabitants of sensitive land use areas from noise pollution. Noise barriers are the most effecti ...
s to effect roadway noise mitigation * modeling of application performance *
flight simulator A flight simulator is a device that artificially re-creates aircraft flight and the environment in which it flies, for pilot training, design, or other purposes. It includes replicating the equations that govern how aircraft fly, how they rea ...
s to train pilots *
weather forecasting Weather forecasting or weather prediction is the application of science and technology forecasting, to predict the conditions of the Earth's atmosphere, atmosphere for a given location and time. People have attempted to predict the weather info ...
* forecasting of risk * simulation of electrical circuits * Power system simulation * simulation of other computers is emulation. * forecasting of prices on financial markets (for example Adaptive Modeler) * behavior of structures (such as buildings and industrial parts) under stress and other conditions * design of industrial processes, such as chemical processing plants *
strategic management In the field of management, strategic management involves the formulation and implementation of the major goals and initiatives taken by an organization's managers on behalf of stakeholders, based on consideration of Resource management, resources ...
and
organizational studies Organization studies (also called organization science or organizational studies) is the academic field interested in a ''collective activity, and how it relates to organization, organizing, and management''. It is "the examination of how individ ...
*
reservoir simulation Reservoir simulation is an area of reservoir engineering in which computer models are used to predict the Fluid dynamics, flow of fluids (typically, oil, water, and gas) through porous media. The creation of models of oil fields and the impleme ...
for the petroleum engineering to model the subsurface reservoir * process engineering simulation tools. * robot simulators for the design of robots and robot control algorithms * urban simulation models that simulate dynamic patterns of urban development and responses to urban land use and transportation policies. * traffic engineering to plan or redesign parts of the street network from single junctions over cities to a national highway network to transportation system planning, design and operations. See a more detailed article on Simulation in Transportation. * modeling car crashes to test safety mechanisms in new vehicle models. * crop-soil systems in agriculture, via dedicated software frameworks (e.g.
BioMA Modelling frameworks are used in Modeling and simulation, modelling and simulation and can consist of a software infrastructure to develop and run Mathematical modelling, mathematical models. They have provided a substantial step forward in the ...
, OMS3, APSIM) The reliability and the trust people put in computer simulations depends on the validity of the simulation
model A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , . Models can be divided in ...
, therefore
verification and validation Verification and validation (also abbreviated as V&V) are independent procedures that are used together for checking that a product, service, or system meets requirements and specification (technical standard), specifications and that it fulf ...
are of crucial importance in the development of computer simulations. Another important aspect of computer simulations is that of reproducibility of the results, meaning that a simulation model should not provide a different answer for each execution. Although this might seem obvious, this is a special point of attention in
stochastic simulation A stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities.DLOUHÝ, M.; FÁBRY, J.; KUNCOVÁ, M.. Simulace pro ekonomy. Praha : VŠE, 2005. Realizations of these ...
s, where random numbers should actually be semi-random numbers. An exception to reproducibility are human-in-the-loop simulations such as flight simulations and
computer games A video game or computer game is an electronic game that involves interaction with a user interface or input device (such as a joystick, game controller, controller, computer keyboard, keyboard, or motion sensing device) to generate visual fe ...
. Here a human is part of the simulation and thus influences the outcome in a way that is hard, if not impossible, to reproduce exactly.
Vehicle A vehicle () is a machine designed for self-propulsion, usually to transport people, cargo, or both. The term "vehicle" typically refers to land vehicles such as human-powered land vehicle, human-powered vehicles (e.g. bicycles, tricycles, velo ...
manufacturers make use of computer simulation to test safety features in new designs. By building a copy of the car in a physics simulation environment, they can save the hundreds of thousands of dollars that would otherwise be required to build and test a unique prototype. Engineers can step through the simulation milliseconds at a time to determine the exact stresses being put upon each section of the prototype.Baase, Sara. A Gift of Fire: Social, Legal, and Ethical Issues for Computing and the Internet. 3. Upper Saddle River: Prentice Hall, 2007. Pages 363–364. .
Computer graphics Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. ...
can be used to display the results of a computer simulation. Animations can be used to experience a simulation in real-time, e.g., in training simulations. In some cases animations may also be useful in faster than real-time or even slower than real-time modes. For example, faster than real-time animations can be useful in visualizing the buildup of queues in the simulation of humans evacuating a building. Furthermore, simulation results are often aggregated into static images using various ways of
scientific visualization Scientific visualization ( also spelled scientific visualisation) is an interdisciplinary branch of science concerned with the visualization of scientific phenomena. Michael Friendly (2008)"Milestones in the history of thematic cartography, st ...
. In debugging, simulating a program execution under test (rather than executing natively) can detect far more errors than the hardware itself can detect and, at the same time, log useful debugging information such as instruction trace, memory alterations and instruction counts. This technique can also detect buffer overflow and similar "hard to detect" errors as well as produce performance information and tuning data.


Pitfalls

Although sometimes ignored in computer simulations, it is very important to perform a
sensitivity analysis Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. This involves estimating sensitivity ...
to ensure that the accuracy of the results is properly understood. For example, the probabilistic risk analysis of factors determining the success of an oilfield exploration program involves combining samples from a variety of statistical distributions using the
Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be ...
. If, for instance, one of the key parameters (e.g., the net ratio of oil-bearing strata) is known to only one significant figure, then the result of the simulation might not be more precise than one significant figure, although it might (misleadingly) be presented as having four significant figures.


See also

*
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, engineering, chemistry and biology to economics ...
*
Digital twin A digital twin is a digital model of an intended or actual real-world physical product, system, or process (a ''physical twin'') that serves as a digital counterpart of it for purposes such as simulation, integration, testing, monitoring, and m ...
* Illustris project * List of computer simulation software * Scene generator *
Simulation A simulation is an imitative representation of a process or system that could exist in the real world. In this broad sense, simulation can often be used interchangeably with model. Sometimes a clear distinction between the two terms is made, in ...
*
Simulation hypothesis The simulation hypothesis proposes that what one experiences as the real world is actually a simulated reality, such as a computer simulation in which humans are constructs. There has been much debate over this topic in the Philosophy, philosophi ...
*
Simulation software Simulation software is based on the process of modeling a real phenomenon with a set of mathematical formulas. It is, essentially, a program that allows the user to observe an operation through simulation without actually performing that operation ...
*
Simulation video game Simulation video games are a diverse super-category of video games, generally designed to closely simulate real world activities. A simulation game attempts to copy various activities from real life in the form of a game for various purposes such ...
* UniverseMachine * Virtual prototyping *
Virtual reality Virtual reality (VR) is a Simulation, simulated experience that employs 3D near-eye displays and pose tracking to give the user an immersive feel of a virtual world. Applications of virtual reality include entertainment (particularly video gam ...
* Web-based simulation


References


Further reading

* Young, Joseph and Findley, Michael. 2014. "Computational Modeling to Study Conflicts and Terrorism.
Routledge Handbook of Research Methods in Military Studies
edited by Soeters, Joseph; Shields, Patricia and Rietjens, Sebastiaan. pp. 249–260. New York: Routledge, * R. Frigg and S. Hartmann
Models in Science
Entry in the ''
Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') is a freely available online philosophy resource published and maintained by Stanford University, encompassing both an online encyclopedia of philosophy and peer-reviewed original publication ...
''. * E. Winsber
Simulation in Science
Entry in the ''
Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') is a freely available online philosophy resource published and maintained by Stanford University, encompassing both an online encyclopedia of philosophy and peer-reviewed original publication ...
''. * S. Hartmann
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 Wolters Kluwer N.V. is a Dutch information services company. The company serves legal, business, tax, accounting, finance, audit, risk, compliance, and healthcare markets. Wolters Kluwer in its current form was founded in 1987 with a merger bet ...
1996, 77–100. * E. Winsberg, ''Science in the Age of Computer Simulation''. Chicago:
University of Chicago Press The University of Chicago Press is the university press of the University of Chicago, a Private university, private research university in Chicago, Illinois. It is the largest and one of the oldest university presses in the United States. It pu ...
, 2010. * P. Humphreys, ''Extending Ourselves: Computational Science, Empiricism, and Scientific Method''. Oxford:
Oxford University Press Oxford University Press (OUP) is the publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books ...
, 2004. * * Desa, W. L. H. M., Kamaruddin, S., & Nawawi, M. K. M. (2012). Modeling of Aircraft Composite Parts Using Simulation. Advanced Material Research, 591–593, 557–560.


External links


Guide to the Computer Simulation Oral History Archive 2003-2018
{{Authority control Computational science Virtual reality Alternatives to animal testing Computational fields of study Computer simulation