Inconsistent variable ranges between original Feynman dataset and feynman.py for dimensionless transformations

[moodyjam]

Summary: The variable ranges in feynman.py differ significantly from the original Feynman dataset, causing issues when transforming to dimensionless equations, particularly when dividing by values near zero.

Background

I am looking and reproducing results from table 2 (Feynman dataset) in the paper. However I am not clear on the ranges of the dimensionless formula inputs. Looking at this issue:
#377
The original Feynman dataset is referenced here, as well as the way to transform the data from the regular formulas to dimensionless ones. However, the ranges of the original equations found in FeynmanEquations.csv are different than the ranges found in feynman.py.

Specific Example

For equation I.15.3x:

• Original ranges (FeynmanEquations.csv): x: [5,10], u: [1,2], c: [3,20], t: [1,2]
• Current ranges (feynman.py): x: [-1,1], u: [-1,1], t: [-1,1], c:[1,2]

The Problem

When doing the variable transformation from FeynmanEquationsDimensionless.csv, my interpretation is that you divide the regular formula by what is in the "Formula" column, in this case: x**1.0. This gives the variable transformations a = t * u / x and b = c / u, giving us the dimensionless equation found in table 2. However if we use the ranges from feynman.py x has range [-1, 1], so we divide by values close to zero. This gives us unreasonable inputs to train on (the original ranges do not have this issue).

Questions

1. How did you transform the regular formulas to dimensionless ones?
2. Are the ranges in feynman.py correct?

[skatayama]

Seemingly feynman.py is not using the dimensionless formula but the original formula. For the example of I.12.11, Table 2 states that the Dimensionless formula is $1 + a \sin \theta$, the variables are $a, \theta$, and thus the number of input units is 2. On the other hand, feynman.py implements it as a 5-ary function.

[moodyjam]

Yes, exactly. However I'm trying to figure out how the authors transformed the original formulas and their ranges from feynman.py into the dimensionless ones. The goal is to reproduce Table 2, but I can't do that without the dimensionless formula ranges.

[skatayama]

Ah, sorry. I commented without reading #377.