I wonder how to choose the number of grids in Kohonen SOM. Also, what will happen when the number of grids increases?
In general, when you increase the number of model parameters, you increase the ability of the model to adapt to more complex problems. For SOMs, this is the case as well. But, the neurons are still connected in a neighborhood relation - so the effect is not linear.
As a practical guide, you can have a look at the documentation of the Python package susi, where the grid size of the SOM, as well as other hyperparameters, are discussed (with literature references): https://susi.readthedocs.io/en/latest/hyperparameters.html