On the Role and Use of Mathematical Models in Engineering Design

Mathematical models encompassing virtually all aspects of engineered products are in widespread use. Indeed, entire industries exist in support of some models: finite element models, computational fluid dynamics models, electric power grid load-flow models, process models, simulation models, and so on. Nonetheless, the purpose, construction, and use of models is not adequately understood. One major issue is that no model perfectly represents reality. Therefore models always diverge from reality somewhere, and they are always inaccurate by some amount. Estimation of model error and the use of model-generated results in support of engineering design decision making are key to the successful use of models.