Presentation of a 2D doubling map with as few "parameters" as possible

Question

I am working on a turn-based game AI using the neural network technique known as NEAT . I am trying to train a network that can move around two-dimensional space (X & Y coords), given the many values ​​that are stored in what is actually a two-dimensional array.

I see two strategies for using a neural network:

• For each "cell" in the grid, specify estimates from different heuristics as contributions to neurons and create NN, which is a very complex scoring system. Move the Non Playing Character (NPC) to the place with the highest score.

• Create a compressed value for each ejuristic measure (somehow compressed as few bits as possible) and providing an input neuron for each of these measures.

I am interested in the second option, because it represents the least amount of necessary calculations (the runtime of the game is quite long), however, I am confused by the approach I could use to create a version of the “small representation” of two-dimensional heuristic values. I know there are methods like Fourier transforms, but I don’t know if they will fit my problem. Basically I am looking for a way to convert a 50x50 doubling array into one or two double values. These two double values ​​can be compressed with losses, I do not need to return the original values, I just need a reasonable mechanism for changing the input data to a small size.

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x = [1:1000];
y = rand(1,1000);
f = fft(y, 250); % truncate to 250 terms
plot(x,y, x,abs(ifft(f), 1000));

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x = [1:1000];
y = rand(1,1000);
f = real(fft(y, 250)); % only uses 1/4 the space now
plot(x,y, x,abs(ifft(f, 1000)));

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