I am trying to use deep learning in order to learn the integral operator. For that I have to take a random function, such that I can apply the anti-derivative and generate my training dataset. I am following a tutorial /link(https://deepxde.readthedocs.io/en/latest/demos/operator/antiderivative_aligned.html) to understand this topic. Here they have taken each data point in the dataset is one pair of $(v,u)$ generated as follows:
A random function $v$ is sampled from a 'Gaussian random field' (GRF) with the resolution $m$ = 100.
What does this mean? I tried searching the internet but could not find an easy explanation for this? Can someone explain this to me with the help of easy terms. What is the exact form of the function which has been used for learning;
like for example if I use $\cos(x) $ then its anti-derivative is $\sin(x) $ ; then I understand that taking points from $\cos(x) $ with known values of $\sin(x) $ and applying my learning on it will help the network understand the anti-derivative operation on this function $\cos(x) $! But what kind of function is being taken here?
Is it such that the learning of the anti-derivative becomes more general than one single function?