Numerical methods are used to simulate the mathematical models of engineering problems. The provided precision is usually fine but at the price of computational cost. This leads us to consider cheap surrogate models in order to reduce the computation time still meeting the precision requirements. We deal herein with the generation of an "optimal" database of pre-calculated results combined with a simple interpolator. Such databases can be used for the approximate solution of both forward and inverse problems. Moreover, their structure carries some meta-information about the involved physical problem.