Why can approximate mathematical models still be useful to systems engineers?

In systems engineering, a mathematical model does not need to be exact to be effective; it only needs to serve its intended purpose. Approximate models are valuable to systems engineers for several key reasons:1

• Practical Utility: Models are simplified representations of the real world that include only relevant variables. Even if a model produces some error, these inaccuracies are often small compared to the significant operational improvements that can be extracted from the model’s insights.2
• Handling Complexity: Many real-world situations are inherently nonlinear. Engineers often use piecewise linear approximations—a series of short straight lines—to represent these complex curves, making them easier to analyze while maintaining sufficient accuracy for decision-making.1
• Efficiency and Optimization: Approximate models allow engineers to perform trade-off studies to determine the most economical way to achieve a goal. They help identify whether a proposed performance target is reasonable or if a modest reduction in performance could lead to radical cost savings.1
• Problem Formulation: Beyond solving specific problems, models act as guides to explore system structures and reveal potential courses of action that might otherwise be overlooked.2