Let's assume I want to teach a CNN some physics. Starting with a U-Net, I input images
B as separate channels. I know that my target (produced by a very slow Monte-Carlo code) represents a signal such as
f(g(A) * h(B)), where
h are fairly "convolutional" operations -- meaning, involving mostly blurring and rescaling operations.
I feel safe to state that this problem would not be too difficult for the case of
f(g(A) + h(B)) -- but what about
f(g(A) * h(B))? Can I expect a basic CNN such as the U-Net to be able to represent the
* (multiplication) operation?
Or should I expect to be forced to include a
Multiply layer in my network, somewhere where I expect that the part before can learn the
h parts, and the part after can learn the