Computer simulation

Because of the computational cost of simulation, computer experiments are used to perform inference such as uncertainty quantification.^[6]

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

• "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;
• 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. 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

• Stochastic or deterministic (and as a special case of deterministic, chaotic) – see external links below for examples of stochastic vs. deterministic simulations
• Steady-state or dynamic
• 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.

• Dynamic simulations attempt to capture changes in a system in response to (usually changing) input signals.
• random number generators
  to model chance or random events;
• A
  discrete event simulation
  (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
  digital computers 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.
• High Level Architecture (simulation) (HLA) and the Test and Training Enabling Architecture
  (TENA).

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.

In science

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

• a numerical simulation of
  roadway air dispersion models), continuum mechanics and chemical kinetics
  fall into this category.
• a
  probabilistically 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, biochemical^[9] or gene regulatory networks with small numbers of molecules. (see also: Monte Carlo method
  ).
• 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 mechanics, Monte Carlo method, 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
  meteorological data to be input for a specific locale. This technique was developed for thermal pollution
  forecasting.
• agent based simulation has been used effectively in ecology, 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 of salmon and trout (most purely mathematical models assume all trout behave identically).
• time stepped dynamic model. In hydrology there are several such
  SWMM and DSSAM Models 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.
• computer simulation using
  molecular modeling for drug discovery.^[10]
• computer simulation to model viral infection in mammalian cells.[9]
• computer simulation for studying the selective sensitivity of bonds by mechanochemistry during grinding of organic molecules.^[11]
• Computational fluid dynamics 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 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: