In the engineering sciences, mathematical models are based on the equations of continuum mechanics, heat flow, Maxwell, Navier-Stokes, or some combination of these. These equations have been validated and their domains of calibration are generally much larger than the expected domain of calibration of the model being developed. In the terminology introduced by Lakatos, the assumptions incorporated in these equations are called hardcore assumptions, and the assumptions incorporated in the other constituents of a model are called auxiliary hypotheses. Model development is concerned with the formulation, calibration, and validation of auxiliary hypotheses.
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