# On the functional form of the radial acceleration relation

arXiv: https://arxiv.org/abs/2301.04368 · HTML: https://mlsanity.com/paper/2301.04368/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 10 references that are in the map.
- First posted on arXiv 11 Jan 2023.

## Built on by (most cited first, 3 of 3)

- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [(Exhaustive) Symbolic Regression and model selection by minimum description length](https://mlsanity.com/paper/2507.13033/) (2025)
- [Constraining dark matter halo profiles with symbolic regression](https://mlsanity.com/paper/2511.23073/) (2025)

## Abstract (arXiv)

We apply a new method for learning equations from data -- Exhaustive Symbolic Regression (ESR) -- to late-type galaxy dynamics as encapsulated in the radial acceleration relation (RAR). Relating the centripetal acceleration due to baryons, gbar, to the total dynamical acceleration, gobs, the RAR has been claimed to manifest a new law of nature due to its regularity and tightness, in agreement with Modified Newtonian Dynamics (MOND). Fits to this relation have been restricted by prior expectations to particular functional forms, while ESR affords an exhaustive and nearly prior-free search through functional parameter space to identify the equations optimally trading accuracy with simplicity. Working with the SPARC data, we find the best functions typically satisfy gobs propto gbar at high gbar, although the coefficient of proportionality is not clearly unity and the deep-MOND limit gobs propto √gbar as gbar → 0 is little evident at all. By generating mock data according to MOND with or without the external field effect, we find that symbolic regression would not be expected to identify the generating function or reconstruct successfully the asymptotic slopes. We conclude that the limited dynamical range and significant uncertainties of the SPARC RAR preclude a definitive statement of its functional form, and hence that this data alone can neither demonstrate nor rule out law-like gravitational behaviour.