Let $f$ be an arbitrary function of $(m+n)$ inputs, i.e. $f(x_1, \cdots, x_m, y_1, \cdots, y_n) \in \mathbb{R}$. We want to compute a definite integral of $f$ over the first $m$ inputs:
$F(y_1, \cdots, y_n)=\int_{\alpha_1}^{\beta_1}\int_{\alpha_2}^{\beta_2}\cdots \int_{\alpha_m}^{\beta_m}f(x_1, \cdots, x_m, y_1, \cdots, y_n)\,dx_m\,dx_{m-1}\cdots dx_1$,
where $\alpha_i$ and $\beta_i$ indicates a (predefined) real range.
Now, assume that there are no analytic solutions, neither for $f$ nor for $F$. But instead we have approximated $f$ with a multilayer perceptron (MLP), $M$.
The question: is there any algorithm that takes $M$ and returns another feedforward NN, $M^\prime$, that computes the function $F$? $\,\,\,$ In other words, can we transform a feedforward neural network into its integration?