[sinuhe69]

And I wonder if somebody has tried with the available galactic data and see if the genetic programming can come up with a better formula than MOND or Einstein's general relativity.

For simple problems as Kepler's law, a quick detour on Desmos will show a perfect fit for power law instantly. In general, there are many important criteria for a better curve fitting (for ex. independent, normal distributed residuals), not just R, so I hope the author has/will incorporate them into the search to create a more robust result.

[sade_95]

Funny you ask, I actually spent a weekend on exactly that. Took the SPARC rotation curve data (~2700 points, 150+ galaxies), built the radial acceleration relation from the raw files and let the engine search. Honest result: it recovered a0 around 1.2e-10 m/s2 like the published fits, and found a different functional form (a log-parabola) that fits exactly as well as the MOND interpolating function, difference of 0.0004 dex. But "exactly as well" is the problem: at the current scatter the data can't tell the forms apart. Which I guess is why the interpolating function debate never dies. No new physics from me, but it was a good way to hit the real wall of the field.

And agreed on residuals, R2 alone is weak. Hold-out validation is already in there, proper residual diagnostics are a fair ask for the roadmap.