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Simulations are used to explore intractable mathematical models or in lieu of empirical experiments which are hard or impossible to conduct for some reason and pilot experiments .

System S provides a core simulation of an object or process B just in case S is a concrete computational device that produces, via a temporal process, solutions to a computational model [...] that correctly represents B, either dynamically or statically. If in addition the computational model used by S correctly represents the structure of the real system R, then S provides a core simulation of system R with respect to B.''

A full simulation in Humphreys' sense is the combination of a core simulation with an output representation.

For humans running simulations, visualizations (output representations) are not just handy—they are actually part of the simulations because without those, humans cannot interpret the results.

According to Humphreys, simulation is a set of techniques rather than a single tool. It includes

• numerical solution of equations,
• visualization,
• error correction on the computational methods,
• data analysis,
• model explorations

Simulations are different from experiments on the real thing', but that is true also of all other kinds of theoretical model.

Computer simulations have benefits over empirical experiments:

• wide ranges of initial conditions can be tested;
• they can be replicated exactly;
• they can be performed where the corresponding experiment would be impossible or unfeasible;
• they are Gedankenexperimente without the psychological biases (well, somewhat);
• they are more amenable to in-depth inspection regarding satisfaction of assumptions—code can be validated, reality cannot;
• they can be used to guide analytical research;

According to Hartmann,

A model is called dynamic, if it... includes assumptions about the time-evolution of the system. ... Simulations are closely related to dynamic models. More concretely, a simulation results when the equations of the underlying dynamic model are solved. This model is designed to imitate the time evolution of a real system. To put it another way, a simulation imitates one process by another process. In this definition, the term process’ refers solely to some object or system whose state changes in time. If the simulation is run on a computer, it is called a computer simulation.''

According to Humphreys, Hartmann's definition of a simulation needs revision, but is basically correct.

In Humphreys' view, simulations need not include evolution over time.

According to Humphreys, the difference between a simulation and a representation or computational model is that it the formulae are evaluated; The formula for an elliptic curve together with parameters (and initial conditions) is a representation of a planetary orbit and a specialized subset of Newtonian physics plus data is a computational model of it. But only the model plus solutions to the formulae for a finite number of time steps is a simulation. (My examples.)

A simulation can be thought of as a thought experiment: Given a correct mathematical model of something, it tries out how that model behaves and translates (via the output representation and interpretation) the behavior back into the realm of the real world.

I would add that a model need not be correct if the simulation is to test the correctness of a model. Then, the thought experiment is to test the hypothesis that the model indeed is correct for the object or process of which it is supposed to be a model by generating predictions (solutions to the mathematical model). Those predictions are then compared to existing behavioral data of the object or process being modeled.

A computer simulation then is a thought experiment carried out by a computer.

According to Sun, it has been argued that models and simulations are only tools to study theories, not theories themselves.

The scientific value of models and simulations has been questioned.

When translating a cognitive theory on the verbal-conceptual level to a computational model, one has to flesh out the description of the model by making decisions.

Some of those decisions are, as Sun says, 'just to make the simulation run', ie. they are arbitrary but consistent with the theory.

Sun argues that a computational model for a verbal-conceptual theory in cognitive science is a theory in itself because it is more specific.

Strictly speaking, every parameterization of an algorithm realizing a computational model distinct from every other parameterization, following Sun's argument.

Sun argues that the failure of one computational model which is a more specific version of a verbal-conceptual theory does not invalidate the theory, especially if a different computational model specifying that theory produces phenomenology consistent with empirical data.

Computer programs are executable and therefore provide a rigorous way of testing their adequacy.

Computer programs can be changed ad-hoc to produce very different kinds of data (by changing production rules or parameters).

One could thus worry about overfitting.

To prevent overfitting, a computational model must be tested against enough data to counter its degrees of freedom.

Jasso and Triesch presented a simulated virtual reality environment for training robotic models.

Jasso and Triesch acknowledge that a simulation does not always follow exactly the laws of physics. In fact, their environment does not simulate any physics except those of human motion.

Jasso and Triesch argue that for the high-level cognition they train, lacking simulations of physics aren't a problem.

Jasso and Triesch argue that their simulated robots are not limited by the capabilities of today's robotic technology.

Computer simulations have been used as early as at least the 1960s to study problems in statistics.

Simulations can lead researchers to postulate unrealistically reliable sensor data or actuation.

Noise in real experiments can make dynamics more stable.

Embodied robots bring together the complexity of sensing and action the real world poses. These are not present in simple models and simulations.