I was actually thinking about this earlier in the day. Could we derive the law of universal gravitation if all we had was a bunch of data about the positions of

I was actually thinking about this earlier in the day. Could we derive the law of universal gravitation if all we had was a bunch of data about the positions of objects at times plus a bunch of machine learning algorithms, and were otherwise complete idiots? But in this case, no, because there's nothing in the particle data that we have that can't already be explained by the standard model, plus any number of other possible models. If only we could find something in the data that we couldn't explain, we might be able to make some progress, but that data doesn't exist.