This is a good question.

A geometrical representation of a Geoid is given in

Hamayan, Global earth structure recovery from state-of-the-art models of the Earth's gravity field and additional geophysical information, Ph.D. thesis, Quad-i-Azam, Pakistan, 2014:

http://www.ncgeo.nl/phocadownload/pdf072014/Thesis_Hamayun.pdf

See Section 2.7, starting on page 16, especially Fig. 2.1 on page 17.  Geodetic coordinates are introduced in Section 2.6, starting on page 14.

In my view, it primarily does not depend on the local topography, however it has some secondary influence. The local geoid can be represented by any number of points, but the values are exact only at those points. Interpolation/collocation algorithms can estimate the geoid position inbetween them and their accuracy is the function of the point density AND the geoid variation characteristic of the area. This latter one is somewhat affected by the topography. (The geoid is an 'weighted average' of the local gravity, which is itself a 'weighted average' of the topography and other factors.)

To turn to practice, in a hilly-low mountain area (e.g. our Hungarian regions), one point per 100 square kilometers provides a vertical accuracy in between the measured points cca. 2 centimeters, which is pretty good for almost all applications. In case of the Himalayas area, I'd expect some decimeters of ambiguity. However, don't forget that in high mountains, especially in steep slopes, the elevation difference between the geoid and the quasi geoid (the base levels of the orthometric and normal heights) can differ also in this range.

When it use an artificial neural network to predicting (interpolation) the most important is that points are patterns that represent the behaviour of the geoid. In this case, is more important the pattern than the points density

Alfonso