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Computer simulation is the running of amathematical model on acomputer, themodel 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. Computersimulations have become a useful tool for the mathematical modeling of many natural systems inphysics (computational physics),astrophysics,climatology,chemistry,biology andmanufacturing, as well as human systems ineconomics,psychology,social science,health care andengineering. 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 newtechnology and to estimate the performance of systems too complex foranalytical solutions.[1]
Computer simulations are realized by runningcomputer programs 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 aroundKuwait, using multiple supercomputers in theDoD High Performance Computer Modernization Program.[2]Other examples include a 1-billion-atom model of material deformation;[3] a 2.64-million-atom model of the complex protein-producing organelle of all living organisms, theribosome, in 2005;[4]a complete simulation of the life cycle ofMycoplasma genitalium in 2012; and theBlue Brain project atEPFL (Switzerland), begun in May 2005 to create the first computer simulation of the entire human brain, right down to the molecular level.[5]
Because of the computational cost of simulation,computer experiments are used to perform inference such asuncertainty quantification.[6]
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".
Computer simulation developed hand-in-hand with the rapid growth of the computer, following its first large-scale deployment during theManhattan Project inWorld War II to model the process ofnuclear detonation. It was a simulation of 12hard spheres using aMonte Carlo algorithm. Computer simulation is often used as an adjunct to, or substitute for, modeling systems for which simpleclosed 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.[7]
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:
Lastly, the time at which data is available varies:
Because of this variety, and because diverse simulation systems have many common elements, there are a large number of specializedsimulation languages. The best-known may beSimula. 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 theaccuracy (compared tomeasurement resolution andprecision) 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"[8] to confirm that values output by the simulation will still be usefully accurate.
Models used for computer simulations can be classified according to several independent pairs of attributes, including:
Another way of categorizing models is to look at the underlying data structures. For time-stepped simulations, there are two main classes:
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.
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 simulationparameters. The use of the matrix format was related to traditional use of the matrix concept inmathematical models. 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 bycomputer-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-cloudcoordinates. 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 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 ofCAT scans can simulate how atumor 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[as of?] to graphically display large amounts of data, in motion, as changes occur during a simulation run.
Generic examples of types of computer simulations in science, which are derived from an underlying mathematical description:
Specific examples of computer simulations include:
Notable, and sometimes controversial, computer simulations used in science include:Donella Meadows'World3 used in theLimits to Growth,James Lovelock'sDaisyworld and Thomas Ray'sTierra.
In social sciences, computer simulation is an integral component of the five angles of analysis fostered by the data percolation methodology,[12] 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[13]
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Computer simulations are used in a wide variety of practical contexts, such as:
The reliability and the trust people put in computer simulations depends on thevalidity of the simulationmodel, thereforeverification and validation 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[editorializing] instochastic simulations, where random numbers should actually be semi-random numbers. An exception to reproducibility are human-in-the-loop simulations such as flight simulations andcomputer games. 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 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.[15]
Computer graphics can be used to display the results of a computer simulation.Animations can be used to experience a simulation in real-time, e.g., intraining 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 ofscientific visualization.
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 detectbuffer overflow and similar "hard to detect" errors as well as produce performance information andtuning data.
Although sometimes ignored in computer simulations, it is very important[editorializing] to perform asensitivity analysis 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 theMonte Carlo method. 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.
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