Yeah, this is the crux. Here's a comment from one of the devs when I asked about the polynomial vs NN basis:
The answer is quite simple really. Classical basis functions suffer from the curse of dimensionality because if you tensor product polynomial basis functions or things like Fourier basis, with N basis functions in each direction, then you have N^d parameters that are required in order to handle every combination `sin(x) + sin(2x) + ... + sin(y) + sin(2y) + ... + sin(x)sin(y) + sin(2x)sin(y) + ....`
The answer is quite simple really. Classical basis functions suffer from the curse of dimensionality because if you tensor product polynomial basis functions or things like Fourier basis, with N basis functions in each direction, then you have N^d parameters that are required in order to handle every combination `sin(x) + sin(2x) + ... + sin(y) + sin(2y) + ... + sin(x)sin(y) + sin(2x)sin(y) + ....`
Neural networks only grow polynomially with dimensional, so at around 8 dimensional objects it becomes more efficient. In fact, this is why we have https://diffeqflux.sciml.ai/dev/layers/BasisLayers/