A model is a simplified description of a more complex phenomenon or process.

Model is a three or two dimensional representation of a anything or of a proposed structure, typically on a smaller scale than the original. e.g. centrifuge modeling. Modeling will similute the real conditions as close as possible so that particular behavior can be predicted precisely.

Thanks to all for your valuable response

The human mind (encapsulating the human intellectual sphere) deals with various intellectual activities such as philosophy, mathematics, the sciences, art, as well as experiences that fall outside of the deliberate, such as unconsciously assimilated experiences falling under the category of intuition. (Damasio 1994). Each domain of the human intellectual sphere is special and recognizable. Philosophy can ask any question while, for example, physics is based on hypotheses, where each of its theories is, more or less, a kind of heuristic MODEL. Mathematics is the science of order, rules, structure and logical connections (many, due to its abstractness, do not classify it as a science but rather in a special domain of the human intellectual sphere; I also have this attitude). We use its discovered abstract regularities in recognizing regularities in our world. In mathematics: If interpretation I happens to make S (sentence) something true then we say that I is a MODEL of S.

It is very difficult to model complex systems with weak emergence.

Complex system has unexpected behavior.In this system The paradoxes arise mostly for the reason that we are often only able to see a part of that system. Considering the complex system (i) we usually embrace the microscopic or the macroscopic level, but not both at once or (ii) we see only the system or the environment, but not both. For physicist and not only for them it is difficult to grasp a complex system with various levels and scales. This difficulty is due to the way how we “see” that information after our brain process it. In other words, it is related to the question of whether the information we obtain about a complex system is subject to the same evolution by randomness and determinism, regardless of context. "So can a combination of chance and determinism produce all the information and everything else we see around us?" It seems to be seen that chance and determinism together underlie every aspect of reality” (Vedral 2010).

This is a very broad question. Let us narrow it towards computer models, which are basically in-computer-program implemented mathematical descriptions of the observed phenomena.

The most difficult models are those describing complex systems and phenomena observed within them: self-organization, emergence, self-replication, self-healing, and similar phenomena. This area of research has a great potential for an explosive development in the near future.

Those phenomena are beyond our current capabilities to successfully understand them and build quickly their relevant models from scratch. We work more or less by using trial and error methods.

In biology and medicine, we observe huge numbers of those phenomena mentioned above. Yet, we are unable to describe them correctly.

When we think about them in depth, we suddenly realize that effective medical treatments of long-term, chronic diseases can be resolved by better and deeper understanding the phenomena under consideration (see above).

This whole area of models, theories, simulations, experiments, and beyond is covered in the projects that are administered by myself and co-authors. (Researchers who are interested are welcomed to check those projects on complexity.)