However, I feel it not an easy job, since enormous factors are concerned. Basicly we can name them into three questions:
First, is our attempting model reflexing well to the reality? In a good situation, these two conceptually coincide and what we need is to eliminate mankind errors, and try to reach most precision; but to a worse case, the model might be totally wrong. This is a question of the nature of model. Second, what form of model it will be? How much we've already know and how much not, and in what manner to represent the two parts respectively? This I call as the physics of model. Third, Are there ways to examine our model's properties such as correctness, robustness, stability? Is there a feedback judgement from the systems we examine and a modification on the model? This can be said the elaboration of model.
From a procedural view, simulation can be separated into system modeling and system identification, two interleaving processes during this work. Many topics are involved and people diver greatly.
On simulation, however, the focus is how to simulate the phenomenon which we can only know from experimental data by a mathematical model to a certain precision. The method for solving uncertainty that I'm interested (or say, my supervisor indicated, :-)) is called interval analysis or known as set membership estimation.
I'm currently studying system identification, numercial resolution to ordinary differential equations, and interval analysis. (These three might form a "why-what-how" structure.) Under the supervision of Mr. Nacim Ramdani. Partial technical report is here.
