At work there is an idea of solving a problem with machine learning. I was assigned the task to have a look at this, since I'm quite good at both mathematics and programming. But I'm new to machine learning.
In the problem a box would be discretized into smaller boxes (e.g. $100 \times 100 \times 100$ or even more), which I will call 'cells'. Input data would then be a boolean for each cell, and output data would be a float for each cell. Thus both input and output have dimensions of order $10^6$ to $10^9$.
Do you have any recommendations about how to do this? I guess that it should be done with a ConvNet since the output depends on relations between close cells.
I have concerns about the huge dimensions, especially as our training data is not at all that large, but at most contains a few thousands of samples.
It can be a bit sensitive to reveal information from a company, but since this is a common problem in computational fluid dynamics (CFD) and we already have a good solution, it might not be that sensitive.
The big boxes are virtual wind tunnels, the small boxes ('cells' or voxels) are a discretization of the tunnel. The input tells where a model is located and the output would give information about where the cells of a volume mesh need to be smaller.