simulations

Simulation is the imitation of the operation of a real-world process or system over time using a model, often implemented as a computer program. A model encodes the key variables, rules, and interactions that govern the system, and a simulator executes the model to generate outputs under specified inputs. Simulations are used to analyze behavior, predict outcomes, test scenarios, train personnel, and support decision making when real experimentation would be costly, dangerous, impractical, or slow.

There are several types of simulations. Physical simulations use tangible scale models or laboratory setups, while digital simulations rely on mathematical models implemented in software. Digital simulations can be further categorized as discrete-event, continuous-time, system dynamics, and agent-based simulations. Data-driven approaches, such as Monte Carlo methods or statistical emulation, are common when uncertainty must be quantified. Verification and validation, along with sensitivity analysis, are essential to assess model fidelity.

Historically, simulation has roots in early scientific computation and the use of physical models, with the Monte Carlo method developed in the 1940s and the growth of computer-based simulations accelerating in aviation, engineering, and science. Today, simulations are pervasive across fields, including engineering design, climate and weather forecasting, urban and traffic planning, finance and economics, medicine, training and education, and entertainment such as computer games and virtual environments. Limitations include model misspecification, data gaps, computational costs, and the need to acknowledge uncertainty and ethical considerations in decision making based on simulations.