# Help! Supervised approach for interpolating a sparse vector field

I am working on an Air Traffic Control problem where the path a plane should take based on its location is given by a vector field. We have a 25x25 grid as seen below, the vectors in red represent input, and the rest of the field is filled out using an optimization approach.

That is we have 5 given vectors (10 values, 1 angle 1 magnitude each) and we interpolate the remaining 625 vectors (1250 values). The optimization approach takes too long however, and we are trying to figure out if we can solve this using a supervised learning approach instead as we already have 10,000 solved samples.

So, each sample is [2, 25, 25] matrix where the first channel holds magnitude and second angle. The input is sparse, that is only 5 spots in each of the channels holds values, the rest are 0’s to be replaced by the network. Here are my questions, I’d appreciate any help on this,

– Is something like this even possible with a supervised approach?
We are trying to learn a predictor which essentially takes 10 values and returns 1250. Is that unreasonable to ask of the network?

– If so, which architecture should I be looking at?
So far I have tried a CNN with an AutoEncoder like structure, several convolutions followed by deconvolutions, with leakyRelu activations to account for all the 0s in my input. The network’s loss goes from 1.6 to around 1.3 and converges, not giving me any useful predictions.