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Exhaustive Symbolic Regression Function Sets

Bartlett, Deaglan J.; Desmond, Harry; Ferreira, Pedro G.

ESR (Exhaustive Symbolic Regression) is a symbolic regression algorithm which efficiently and systematically finds all possible equations at fixed complexity (defined to be the number of nodes in its tree representation) given a set of basis functions. This is achieved by identifying the unique equations, so that one minimises the number of equations which one would have to fit to data.

Here we provide the functions generated, the unique equations, and the mappings between all equations and unique ones using different sets of basis functions. These are:

  • "core_maths": \(\{x, a, {\rm inv}, +, -, \times, \div, {\rm pow} \}\)
  • "ext_maths": \(\{x, a, {\rm inv}, \sqrt{\cdot}, {\rm square}, \exp, +, -, \times, \div, {\rm pow} \}\)

where \(x\) is the input variable and \(a\) denotes a constant.

One can fit these functions to a data set of interest by using the ESR package.

DJB is supported by the Simons Collaboration on ``Learning the Universe'' and was supported by STFC and Oriel College, Oxford. HD is supported by a Royal Society University Research Fellowship (grant no. 211046). PGF acknowledges support from European Research Council Grant No: 693024 and the Beecroft Trust.
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