I think that your question is geared more as to how a model can describe the general features of an underlying physical phenomenon and how can it be translated to an algorithm. The level of detail of the model ( and its implementation in an algorithm) depends on the person analyzing the mode, how does he think it captures the desired level of complexity, and what are the questions that he wants to address in his research. For example, most neural network models used in machine learning abstract the underlying chemical process. The question is: does it matter to the results obtained on a dataset? It all depends on what is the underlying question that you want to answer.

The model (and its underlying algorithm) should capture enough detail so that it explains the underlying phenomenon but not so much that it makes it totally useless.