Deep learning toolbox for approximation of functions

Hi there,

I am having a dataset of N number of points for each input and output. I need to approximate the functions as below. Deep learning toolbox is pretty new to me and often see examples of image classification/processing. Can someone please give me some suggestions of the tools/Matlab functions, which are the most advanced, that fit for my application? I wanted to first try to use the up-to-date progress of deep learning in a quick-and-dirty way with Matlab to solve my problem.

Thanks,

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a1*f(x1, y1)+b1*g(x1,y1)+c1*h(x1,y1)+d1*k(x1,y1) = z1

a2*f(x2, y2)+b2*g(x2,y2)+c2*h(x2,y2)+d2*k(x2,y2) = z2

....

aN*f(xN, yN)+b1*g(xN,yN)+cN*h(xN,yN)+dN*k(xN,yN) = zN

All parameters, inputs, output a1->aN, b1->bN, c1->cN, d1->dN, x1->xN, y1->xN, z1->zN are known data points. The problem is how to find out the approximate functions f, g, h, k

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