Computer simulation

A computer simulation begins with a mathematical model that describes the system's state and the rules governing its change over time. The model is implemented as a program that advances time in discrete steps or continuously, generating a trajectory of states. Validation and verification are critical: verification ensures the code correctly implements the model, while validation checks that the model accurately represents the real system.² Simulations often use random number generation to represent stochastic processes, leading to Monte Carlo methods that estimate probabilities by repeated sampling.³

Simulations are classified by how time and state are handled: discrete-event simulation models systems where changes occur at distinct times (e.g., queueing networks), while continuous simulation uses differential equations for smooth processes (e.g., fluid dynamics). Agent-based models simulate the actions of individual entities to observe emergent collective behavior, used in economics and ecology.⁴ Applications span weather forecasting, climate modeling, drug discovery, autonomous vehicle testing, and social science. In engineering, finite element analysis simulates stress and heat to reduce physical prototyping.⁵

The earliest computer simulations were developed during the Manhattan Project in the 1940s to model neutron transport, using Monte Carlo methods on early electronic computers.⁶ In the 1950s, the first simulation languages, such as GPSS and SIMULA, made the technique accessible to a wider audience. The rise of personal computers and graphical interfaces in the 1980s brought simulation to desktop users, while the advent of high-performance computing and cloud platforms in the 2000s enabled massively parallel simulations of complex systems like global climate.⁷

Beyond mainstream uses, simulations have niche applications: in archaeology, they model ancient population dynamics; in sports, they predict game outcomes; in finance, they stress-test portfolios. A notable edge case is the "simulation of a simulation" used in testing quantum computers. The concept of "digital twins" — real-time simulations of physical assets — is a growing field. Also, the first computer simulation of a human heart was performed in the 1960s, and simulations of nuclear weapons have been used to verify the stockpile without testing.

Monte Carlo method

A technique that uses random sampling to obtain numerical results, often for estimating probabilities.

Discrete-event simulation

A simulation where state changes occur at specific points in time.

Agent-based model

A simulation of autonomous agents interacting to observe emergent patterns.

Digital twin

A virtual replica of a physical system that is updated with real-time data.