5 - Strategies for simplifying mathematical models

Summary

A mathematical model can never give an exact description of the real world, and the basic concept in all engineering modeling is, “All models are wrong – some models are useful.” Reformulating or simplifying the models is not tampering with the truth. You are always allowed to change the models, as long as the results are within an acceptable range. It is the objective of the modeling that determines the required accuracy: Is it a conceptual study limited to order of magnitude estimations? Or is it design modeling in which you will add 10–25% to the required size in order to allow for inaccuracies in the models and future increase in production? Or is it an academic research work that you will publish with as accurate simulations as possible?

A simulation may contain both errors and uncertainties. An error is defined as a recognizable deficiency that is not due to lack of knowledge, and an uncertainty is a potential deficiency that is due to lack of knowledge. All simulations must be validated and verified in order to avoid errors and uncertainties. Validation and verification are two important concepts in dealing with errors and uncertainties. Validation means making sure that the model describes the real world correctly, and verification is a procedure to ensure that the model has been solved in a correct way.