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Lets pretend that I didnt know newtons law of gravitation

https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation

but I had data for all variables (F,m1,m2,r)

Is there any tooling that will just iterate through lots of different equations until it arrives that the correct formula?

another example - lets say I didn't know how to do a 3D rotation

https://en.wikipedia.org/wiki/Rotation_matrix

but I have lots of data. Any machine learning that could spit out the exact formula?

user378380
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    At https://stats.stackexchange.com/questions/35711/box-cox-like-transformation-for-independent-variables/35717#35717 I give an example of how a physical law is not only systematically discovered, but even improved upon using basic techniques of exploratory data analysis. It involves *intelligently choosing* analytical options rather than blindly iterating through a large number of formulas. – whuber Jul 03 '18 at 21:02

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No. For any finite set of data points, there are an infinite number of equations that will fit the data perfectly, so an automated procedure would have no way of telling which of those infinite equations is the correct or even the best one.

Even if you had a tool with a large but finite set of equations and it tried fitting each of those, if your data is measured, recorded, or entered with any kind of uncertainty then there is a chance (high chance if there are enough equations in your set of possibilities) that the best model will not be the correct model.

Statistics and computing are not excuses to not think. They are tools to combine with your knowledge of the background and subject.

Greg Snow
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