## FANDOM

186 Pages

For modeling, there are two important factors which are accuracy and complexity. Two factors are on the relatioship of tradeoff. That is, if one of them is changed the optimal value of the other would be revised.

In this article, we propose to consider information theory to represent the performance of modeling results. By applying infromation theory for modeling, we can represents two factors in modeling more quantitatively.

Information theory has been used for a signal which is less general than a model, but it is highly obvious that a signal is one of the source to be represented by modeling such as digital value modeling of analog signal.

## Computational ScienceEdit

The goal of computational science is to accelerate the development of various fields of science and technology using information technology.

## Modeling PerformanceEdit

For modeling, there are two important factors which are accuracy and complexity. Two factors are related to each other. That is, if one of them is changed the optimal value of the other would be revised.

### Modeling Accuracy Edit

Based on the information theory, the accuracy of modeling can be represented by the term of distortion.

## Limit of information theory for representing the modeling performanceEdit

Differently from the general representation of information signals, the performance of modeling technology is also related to the computational complexity. The modeling formulation is described usually mathematical equations, while the signal is represented as digital information or binary bits.

### Similarity between modeling and information Edit

There are also similarity in two different areas of signal representations and models. Signal can also be represented by some formulations such as $x = \sin( t)$. Although this formulation can be represented by the finite information, the signal generated by this formulation goes to be infinitive if we do not fix the rage of time $t$. Hence, in this case, Fourier transform can be used to pack the information. After the Fourier transformation of the signal generated by the formulation of $x = \sin( t)$, the required amount of information to represent the frequency domain information of it becomes a limited value assuming we fixed the frequency range and resolution within interesting bounds.

### Limit of infromation theory to analize the modeling performance Edit

Let us assume that we consider non-regular nonlinear formations such as $x = t^2$. This information is not well packed by the Fourier transformation. Hence, the amount of this information would be huge (or infinitive if time scale is not fixed) if we represent its output signal instead of the formulation directly. Hence, the comparison between the original signal and the generated signal becomes not efficient if the comparison is performed only by information theory. Hence, we can conclude that for the effective analysis of the modeling performance we need to develop new theory which overcomes the limitation of information theory.

## Modeling TheoryEdit

I propose to build up modeling theory which includes new effective methods to analysis the modeling performance.