Why must a mathematical model represent the real physical situation well?

In systems engineering, a mathematical model must represent a physical situation well enough to serve its intended purpose, though it does not need to be an exact replica of reality. Because real-world systems are often complex, engineers use models to describe interactions in quantitative terms, allowing them to analyze system operations, perform trade-offs, and identify the most economical ways to achieve goals.12

A model must be sufficiently accurate to provide reliable insights into the actual operation of a system, such as predicting performance or determining if a proposed goal is reasonable. While models often rely on simplifications—such as using piecewise linear approximations for nonlinear situations—these approximations must correctly incorporate the most important features of the physical situation. If a model fails to account for essential variables, it can lead to incorrect conclusions.132

Ultimately, the goal is to balance complexity and utility; engineers refine models through systematic procedures, such as perturbation techniques, to ensure they represent the physical situation closely enough to be useful for design and decision-making without becoming impossibly complicated.3