If you define the optimization objective to be y = m . x1 . x2 . x3^-2, or perhaps the family y = m . x1^a . x2^b . x3^c -- you might be able to select the right function based on an "experimentally prepared" dataset.
That dataset would not be photographs of the night sky, and those models you're fitting would have to be pre-specified.
We can show, easily, no automated statistical modelling of the night sky will produce F=GMm/r^2
The optimization objective for automated modelling here makes the resulting model nothing more than an interpolation through data points.
Those points, the position of the planets in the sky say, are not caused by F=GMm/r^2 -- but by a near-infinite nuumber of causes, including our relative positions to those planets *which is not in the night sky!*.
If you already know the form of the answer, and have already done the right experiments, yes: the solution is function optimization
That dataset would not be photographs of the night sky, and those models you're fitting would have to be pre-specified.
We can show, easily, no automated statistical modelling of the night sky will produce F=GMm/r^2
The optimization objective for automated modelling here makes the resulting model nothing more than an interpolation through data points.
Those points, the position of the planets in the sky say, are not caused by F=GMm/r^2 -- but by a near-infinite nuumber of causes, including our relative positions to those planets *which is not in the night sky!*.
If you already know the form of the answer, and have already done the right experiments, yes: the solution is function optimization