Training a Variational Autoencoder (VAE) for Random Number Generation I have a complicated 20-dimensional multi-modal distribution and consider training a VAE to learn an approximation of it using 2000 samples. But particularly, with the aim to subsequently generate pseudo-random numbers behaving according to the structure of the distribution. However, my problems are the following:

Is my approach fundamentally or logically flawed? Specifically, because unlike image data, the random numbers are of geometric nature and thus take negative values and could also be considered noisy.
How do I find the right architecture aside from simple trial and error? Obviously, I do not necessarily need 2D-Convolutions. But instead, 1D-Convolutions could be considered a good choice to capture the correlations (i.e. modalities of the distribution). I'm also not sure about how I properly decide on the number of hidden layers and nodes.
You are describing surrogate modelling.
Because your situation is well studied, I recommend looking at what others have published. See, this paper for example.