Approximation of non-linearities

Question

I have the following differential equation $$\ddot q=M^{-1}(q) (C(q,\dot q)\dot q+G(q))+M^{-1}(q)u+M^{-1}(q)D(t) $$ The author of the textbook refers to the terms $M^{-1}(q) (C(q,\dot q)\dot q+G(q))$ and $M^{-1}(q)$ as unknown non-linearities although they have no unknown parameters other than $q$ and $\dot q$ and then states that we can approximate them using neural networks. What is a non-linearity in this case and why do we need to approximate it?

Answer 1

It seems like, although in the given example these terms have known values,the author wanted to generalize the solution of such problems for the case that these terms function like "black boxes" and are thus considered unknown and can be approximated by their inputs and outputs.