Find an equation with a set of solutions?

Question

Mathematics

I don’t know how to ask a question, see if there is or is not a section in mathematics, all I find is a school course.
In short, there is an infinite set of points (x,y) for example, and is there a way to get some very very complex equation that describes this set of solutions, at least approximately.
That is, the inverse problem is to plot the graph according to the equation.

Answer 1

Infinite - no.
Ultimately, yes.
If this is a set of experimental data, there is a general formula and it is necessary to select coefficients, then the least squares method is usually used.

Answer 2

No.
There is no straight forward solution.
You can use your experience to look at the graph and infer the nature and composition of the equation.
In other words, the answer is to use brute force and neural networks (which still need to be trained to recognize graphs). You yourself, that is, your brain, or rather the brain of a mathematics professor, is, in fact, a large and complex neural network that solves such complex problems.
But even a genius is unlikely to come up with an equation for something like this:

spoiler