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This article seems to be about ML but good old fashioned brute force searches are also possible. It's trivial to find formulas that fit data to within the vari
by kloch 4y ago
This article seems to be about ML but good old fashioned brute force searches are also possible.
It's trivial to find formulas that fit data to within the variable's uncertainties. You can easily drown in such output. There are two main challenges with this approach: 1. make sure you have the right "ingredients" (factors) for the search, and 2. filter the output so that human reviewers don't waste time on obvious nonsense equations.
Filtering output is not terribly difficult. Some assessment of complexity is required and depending on the formula a symmetry score might be useful. Some actual physics equations are quite complex so you have to be expecting a simple equation or filtering output will be less effective.
Making sure you have all of the right potential factors available is very hard. Expanding the input factor set extends the search space and time.
- ChrisRackauckas 4y agoBrute force costs grow exponentially (well, combinatorically) with the number of terms. It's viable for the small cases, but not for the larger cases. There's a nice paper from 2016 which demonstrates this very directly (http://www.cogsys.org/proceedings/2016/paper-2016-2.pdf http://www.cogsys.org/proceedings/2016/paper-2016-2.pdf), though I'm sure there's some stuff from the 70's on it as well.