Specifications of the substrates are among the most important and problematic parameters that still do not have proper models in the design procedures of metasurfaces. In this paper, a new fast and exact algorithm based on artificial neural networks (ANNs) is presented, which makes it possible to design frequency-selective surfaces (FSSs) on various kinds of standard substrates. Also for the first time, designing FSSs on uniaxial anisotropic substrates can be easily done in short time and without any optimization algorithms. During this paper, first equivalent geometry approach (EGA) is demonstrated as a new method of preparation the ANNs. Then EGA is used to train geometry transformation ANNs. The advantage of this approach is to reduce the size of training datasets by about 98% and prevent from superfluous simulations. Hence, the time needed for training of the networks is much less than before. Numerical results are used to show that the required time for developing FSSs is <200 ms on average, and errors are <2%. For the final validation, a prototype sample of FSS is fabricated on the RO4003 substrate with 20 mil thickness. Both analytical and experimental results confirm the correctness of the predicted values.