A computer simulation, a computer model, or a computational model is a computer program A computer program is a sequence of instructions written to perform a specified task for a computer. A computer requires programs to function, typically executing the program's instructions in a central processor. The program has an executable form that the computer can use directly to execute the instructions. The same program in its human-, or network of computers, that attempts to simulate Simulation is used in many contexts, including the modeling of natural systems or human systems in order to gain insight into their functioning. Other contexts include simulation of technology for performance optimization, safety engineering, testing, training and education. Simulation can be used to show the eventual real effects of alternative an abstract model In the most general sense, a model is anything used in any way to represent anything else. Some models are physical objects, for instance, a toy model which may be assembled, and may even be made to work like the object it represents. However a conceptual model, may only be drawn on paper, described in words, or imagined in the mind. They are used of a particular system. Computer simulations have become a useful part of mathematical modeling A mathematical model uses mathematical language to describe a system. The process of developing a mathematical model is termed mathematical modelling . Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines, but also in the social sciences (such as economics, of many natural systems in physics Physics is a natural science that involves the study of matter and its motion through space-time, as well as all applicable concepts, such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves (computational physics Computational physics is the study and implementation of numerical algorithms to solve problems in physics for which a quantitative theory already exists. It is often regarded as a subdiscipline of theoretical physics but some consider it an intermediate branch between theoretical and experimental physics), astrophysics Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature, and chemical composition) of celestial objects such as galaxies, stars, planets, exoplanets, and the interstellar medium, as well as their interactions. The study of cosmology addresses questions, chemistry Chemistry is the science of matter and the changes it undergoes. The science of matter is also addressed by physics, but while physics takes a more general and fundamental approach, chemistry is more specialized, being concerned with the composition, behavior, structure, and properties of matter, as well as the changes it undergoes during chemical and biology Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy, human systems in economics Economics is the social science that is concerned with the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek οἰκονομία from οἶκος (oikos, "house") + νόμος (nomos, "custom" or "law"), hence "rules of the house(hold)". Current, psychology Psychology is the scientific study of human or other animal mental functions and behaviors. In this field, a professional practitioner or researcher is called a psychologist. Psychologists are classified as social or behavioral scientists. Psychological research can be considered either basic or applied. Psychologists attempt to understand the, social science The social sciences are the fields of academic scholarship that explore aspects of human society. "Social science" is commonly used as an umbrella term to refer to a plurality of fields outside of the natural sciences. These include: anthropology, archaeology, economics, geography, history, linguistics, political science, international, and engineering Engineering is the discipline, art and profession of acquiring and applying technical, scientific, and mathematical knowledge to design and implement materials, structures, machines, devices, systems, and processes that safely realize a desired objective or invention. Simulations can be used to explore and gain new insights into new technology Technology is a term referring to whatever can be said at any particular historical period, concerning the state of the art in the whole general field of practical know-how and tool use. It therefore encompasses all that can be said about arts, crafts, professions, applied sciences, and skills. By extension it can also refer to any systems or, and to estimate the performance of systems too complex for analytical solutions. [1]

Computer simulations vary from computer programs that run a few minutes, to network-based groups of computers running for hours, to ongoing simulations that run for days. The scale of events being simulated by computer simulations has far exceeded anything possible (or perhaps even imaginable) using the traditional paper-and-pencil mathematical modeling A mathematical model uses mathematical language to describe a system. Mathematical models are used not only in the natural sciences and engineering disciplines but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most: over 10 years ago, 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 The State of Kuwait is a sovereign Arab emirate situated in the northeast of the Arabian Peninsula in Western Asia. It is bordered by Saudi Arabia to the south and Iraq to the north and lies on the northwestern shore of the Persian Gulf. The name Kuwait is derived from the Arabic "akwat", the plural of "kout", meaning fortress, using multiple supercomputers in the DoD The United States Department of Defense is the U.S. federal department charged with coordinating and supervising all agencies and functions of the government relating directly to national security and the United States armed forces. The organization and functions of the DOD are set forth in Title 10 of the United States Code High Performance Computer Modernization Program; [2] a 1-billion-atom model of material deformation (2002); a 2.64-million-atom model of the complex maker of protein in all organisms, a ribosome Ribosomes are the components of cells that make proteins from amino acids. One of the central tenets of biology, often referred to as the "central dogma," is that DNA is used to make RNA, which, in turn, is used to make protein. The DNA sequence in genes is copied into a messenger RNA . Ribosomes then read the information in this RNA and, in 2005;[3] and the Blue Brain The aim of the project, founded in May 2005 by the Brain and Mind Institute of the École Polytechnique in Lausanne, Switzerland, is to study the brain's architectural and functional principles. The project is headed by the Institute's director, Henry Markram. Using a Blue Gene supercomputer running Michael Hines's NEURON software, the simulation project at EPFL The École Polytechnique Fédérale de Lausanne is one of the two Swiss Federal Institutes of Technology and is located in Lausanne, Switzerland. EPFL is ranked as Europe's number 1 and world's number 15 university in the field of "Engineering/Technology and Computer Sciences" in the academic ranking of world universities (ARWU) by (Switzerland), began in May 2005, to create the first computer simulation of the entire human brain, right down to the molecular level. [4]

Contents

Simulation versus modeling

Traditionally, forming large models of systems has been via a mathematical model A mathematical model uses mathematical language to describe a system. The process of developing a mathematical model is termed mathematical modelling . Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines, but also in the social sciences (such as economics,, which attempts to find analytical solutions In mathematics, an expression is said to be a closed-form expression if, and only if, it can be expressed analytically in terms of a bounded number of certain "well-known" functions. Typically, these well-known functions are defined to be elementary functions – constants, one variable x, elementary operations of arithmetic , nth roots, to problems and thereby enable the prediction of the behavior of the system from a set of parameters and initial conditions.

While computer simulations might use some algorithms from purely mathematical models, computers can combine simulations with reality or actual events, such as generating input responses, to simulate test subjects who are no longer present. Whereas the missing test subjects are being modeled/simulated, the system they use could be the actual equipment, revealing performance limits or defects in long-term use by these simulated users.

Note that the term computer simulation is broader than computer modeling, which implies that all aspects are being modeled in the computer representation. However, computer simulation also includes generating inputs from simulated users to run actual computer software or equipment, with only part of the system being modeled: an example would be flight simulators A flight simulator is a system that tries to copy, or simulate, the experience of flying an aircraft. It is meant to be as realistic as possible. The different types of flight simulator range from computer based games up to full-size cockpit replicas mounted on hydraulic actuators, controlled by state of the art computer technology which can run machines as well as actual flight software.

Computer simulations are used in many fields, including science Science is a systematic enterprise of gathering knowledge about nature and organizing and condensing that knowledge into testable laws and theories. As knowledge has increased, some methods have proved more reliable than others, and today the scientific method is the standard for science. It includes the use of careful observation, experimentation,, technology Technology is a term referring to whatever can be said at any particular historical period, concerning the state of the art in the whole general field of practical know-how and tool use. It therefore encompasses all that can be said about arts, crafts, professions, applied sciences, and skills. By extension it can also refer to any systems or, entertainment Entertainment consists of any activity which provides a diversion or permits people to amuse themselves in their leisure time. Entertainment is generally passive, such as watching opera or a movie. Active forms of amusement, such as recreations or sports, are more often considered to be recreation. Activities such as personal reading or practicing, health care, and business A business is a legally recognized organization designed to provide goods or services, or both, to consumers, businesses and governmental entities. Businesses are predominant in capitalist economies. Most businesses are privately owned. A business is typically formed to earn profit that will increase the wealth of its owners and grow the business planning and scheduling.

History

Computer simulation was 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 the codename for a project conducted during World War II to develop the first atomic bombs. The project was led by the United States, and included participation from the United Kingdom and Canada. Formally designated as the Manhattan Engineering District , it refers specifically to the period of the project from 1942–194 in World War II Albania · Australia · Austria · Azerbaijan · Belarus · Belgium · Brazil · Bulgaria · Burma · Cambodia · Canada · Ceylon (Sri Lanka) · Channel Islands · China · Czechoslovakia · Denmark · Dutch East Indies · Egypt · Estonia · Finland · France · Germany · Gibraltar · Greece · Greenland · Hong Kong · Hungary · Iceland · to model the process of nuclear detonation A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission or a combination of fission and fusion. Both reactions release vast quantities of energy from relatively small amounts of matter; a modern thermonuclear weapon weighing little more than a thousand kilograms can produce an explosion. It was a simulation of 12 hard spheres using a Monte Carlo algorithm Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in simulating physical and mathematical systems. Because of their reliance on repeated computation of random or pseudo-random numbers, these methods are most suited to calculation by a. Computer simulation is often used as an adjunct to, or substitution for, modeling systems for which simple closed form analytic solutions In mathematics, an expression is said to be a closed-form expression if, and only if, it can be expressed analytically in terms of a bounded number of certain "well-known" functions. Typically, these well-known functions are defined to be elementary functions – constants, one variable x, elementary operations of arithmetic , nth roots, are not possible. There are many different types of computer simulation; the common feature they all share 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. Computer models were initially used as a supplement for other arguments, but their use later became rather widespread.

Data preparation

Main article: Simulation language

The data input/output for the simulation can be either through formatted textfiles or a pre- and postprocessor.

Data preparation is possibly the most important aspect of computer simulation. Since the simulation is digital with the inherent necessity of rounding/truncation error, even small errors in the original data can accumulate into substantial error later in the simulation. While all computer analysis is subject to the "GIGO" (garbage in, garbage out) restriction, this is especially true of digital simulation. Indeed, it was the observation of this inherent, cumulative error, for digital systems that is the origin of chaos theory Chaos theory is a field of study in mathematics, physics, economics and philosophy studying the behavior of dynamical systems that are highly sensitive to initial conditions. This sensitivity is popularly referred to as the butterfly effect. Small differences in initial conditions yield widely diverging outcomes for chaotic systems, rendering long-.

Types

Computer models can be classified according to several independent pairs of attributes, including:

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.

CGI computer simulation

Formerly, the output data from a computer simulation was sometimes presented in a table, or a matrix, showing how data was 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 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 by computer-generated-imagery (CGI) animation. Although observers couldn't necessarily read out numbers, or spout 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 scanning tables of rain-cloud coordinates. 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 of CAT scans can simulate how a tumor 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.

Computer simulation in science

Generic examples of types of computer simulations in science, which are derived from an underlying mathematical description:

Specific examples of computer simulations follow:

Notable, and sometimes controversial, computer simulations used in science include: Donella Meadows' World3 used in the Limits to Growth, James Lovelock's Daisyworld and Thomas Ray's Tierra.

Simulation environments for physics and engineering

Graphical environments to design simulations have been developed. Special care was taken to handle events (situations in which the simulation equations are not valid and have to be changed). The open project Open Source Physics was started to develop reusable libraries for simulations in Java, together with Easy Java Simulations, a complete graphical environment that generates code based on these libraries.

Computer simulation in practical contexts

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 the validity of the simulation model, therefore verification 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 in stochastic simulations, 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. 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 a unique prototype and test it. Engineers can step through the simulation milliseconds at a time to determine the exact stresses being put upon each section of the prototype.[5]

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. 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.

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 sensitivity analysis to ensure that the accuracy of the results are 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. If, for instance, one of the key parameters (i.e. 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.

Model Calibration Techniques

The following three steps should be used to produce accurate simulation models: calibration, verification, and validation. Computer simulations are good at portraying and comparing theoretical scenarios but in order to accurately model actual case studies, it has to match what is actually happening today. A base model should be created and calibrated so that it matches the area being studied. The calibrated model should then be verified to ensure that the model is operating as expected based on the inputs. Once the model has been verified, the final step is to validate the model by comparing the outputs to historical data from the study area. This can be done by using statistical techniques and ensuring an adequate R-squared value. Unless these techniques are employed, the simulation model created will produce inaccurate results and not be a useful prediction tool.

Model calibration is achieved by adjusting any available parameters in order to adjust how the model operates and simulates the process. For example in traffic simulation, typical parameters include look-ahead distance, car-following sensitivity, discharge headway, and start-up lost time. These parameters influence driver behaviors such as when and how long it takes a driver to change lanes, how much distance a driver leaves between itself and the car in front of it, and how quickly it starts to accelerate through an intersection. Adjusting these parameters has a direct effect on the amount of traffic volume that can traverse through the modeled roadway network by making the drivers more or less aggressive. These are examples of calibration parameters that can be fine-tuned to match up with characteristics observed in the field at the study location. Most traffic models will have typical default values but they may need to be adjusted to better match the driver behavior at the location being studied.

Model verification is achieved by obtaining output data from the model and comparing it to what is expected from the input data. For example in traffic simulation, traffic volume can be verified to ensure that actual volume throughput in the model is reasonably close to traffic volumes input into the model. Ten percent is a typical threshold used in traffic simulation to determine if output volumes are reasonably close to input volumes. Simulation models handle model inputs in different ways so traffic that enters the network, for example, may or may not reach its desired destination. Additionally, traffic that wants to enter the network may not be able to if any congestion exists. This is why model verification is a very important part of the modeling process.

The final step is to validate the model by comparing the results with what’s expected based on historical data from the study area. Ideally, the model should produce similar results to what has happened historically. This is typically verified by nothing more than quoting the R2 statistic from the fit. This statistic measures the fraction of variability that is accounted for by the model. A high R2 value does not necessarily mean the model fits the data well. Another tool used to validate models is graphical residual analysis. If model output values are drastically different than historical values, it probably means there’s an error in the model. This is an important step to verify before using the model as a base to produce additional models for different scenarios to ensure each one is accurate. If the outputs do not reasonably match historic values during the validation process, the model should be reviewed and updated to produce results more in line with expectations. It is an iterative process that helps to produce more realistic models.

Validating traffic simulation models requires comparing traffic estimated by the model to observed traffic on the roadway and transit systems. Initial comparisons are for trip interchanges between quadrants, sectors, or other large areas of interest. The next step is to compare traffic estimated by the models to traffic counts, including transit ridership, crossing contrived barriers in the study area. These are typically called screenlines, cutlines, and cordon lines and may be imaginary or actual physical barriers. Cordon lines surround particular areas such as the central business district or other major activity centers. Transit ridership estimates are commonly validated by comparing them to actual patronage crossing cordon lines around the central business district.

Three sources of error can cause weak correlation during calibration: input error, model error, and parameter error. In general, input error and parameter error can be adjusted easily by the user. Model error however is caused by the methodology used in the model and may not be as easy to fix. Simulation models are typically built using several different modeling theories that can produce conflicting results. Some models are more generalized while others are more detailed. If model error occurs as a result of this, in may be necessary to adjust the model methodology to make results more consistent.

In order to produce good models that can be used to produce realistic results, these are the necessary steps that need to be taken in order to ensure that simulation models are functioning properly. Simulation models can be used as a tool to verify engineering theories but are only valid if calibrated properly. Once satisfactory estimates of the parameters for all models have been obtained, the models must be checked to assure that they adequately perform the functions for which they are intended. The validation process establishes the credibility of the model by demonstrating its ability to replicate actual traffic patterns. The importance of model validation underscores the need for careful planning, thoroughness and accuracy of the input data collection program that has this purpose. Efforts should be made to ensure collected data is consistent with expected values. For example in traffic analysis, it is typically common for a traffic engineer to perform a site visit to verify traffic counts and become familiar with traffic patterns in the area. The resulting models and forecasts will be no better than the data used for model estimation and validation.

References

This article includes a list of references or external links, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations where appropriate. (May 2008)
  1. ^ Strogatz, Steven (2007), "The End of Insight", in Brockman, John, What is your dangerous idea?, HarperCollins, ISSN 9780061214950
  2. ^ " "Researchers stage largest Military Simulation ever", Jet Propulsion Laboratory, Caltech, December 1997,
  3. ^ "Largest computational biology simulation mimics life's most essential nanomachine" (news), News Release, Nancy Ambrosiano, Los Alamos National Laboratory, Los Alamos, NM, October 2005, webpage: LANL-Fuse-story7428.
  4. ^ "Mission to build a simulated brain begins", project of the institute at the École Polytechnique Fédérale de Lausanne (EPFL), Switzerland, New Scientist, June 2005.
  5. ^ 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. ISBN 0-13-600848-8.

Notes

External links

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Organizations

Education

Examples

Techniques to analyze computer simulations

Categories: Computational science | Scientific modeling | Simulation software | Virtual reality

 

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Spiritually speaking, Is it possible for the entire universe to be a high-end computer simulation program?
Q. And the scientists that have the program can stream forwards and backwards as they wish, and see how the worlds evolved, etc. The computer could calculate events in fraction of milliseconds, and the Scientists could look around freely, and we would be oblivious to the fact. Does this mean our life is milliseconds long? *Please do not compare this to the matrix, I hate that movie and did not get this idea from it*
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A. It is possible, but unlikely. That said, we tend to be "programmed" by more than just our heritage and experiences. Our behavioral patters are very diverse, and yet, the more we understand about a person and what they do, why they do it, and so on, the more we can "predict" their actions in any given situation. God could be one master programmer! (LOL) Disclaimer: My response to this question does not reflect my thinking (belief) on the nature of life.
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