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, $g_\text{bar}$, to the total dynamical acceleration, $g_\text{obs}$, 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 $g_\text{obs} \propto g_\text{bar}$ at high $g_\text{bar}$, although the coefficient of proportionality is not clearly unity and the deep-MOND limit $g_\text{obs} \propto \sqrt{g_\text{bar}}$ as $g_\text{bar} \to 0$ 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.

翻译：我们应用一种从数据中学习方程的新方法——穷举符号回归（ESR）——来研究晚型星系动力学，具体体现在径向加速度关系（RAR）中。该关系将重子物质导致的向心加速度 $g_\text{bar}$ 与总动力学加速度 $g_\text{obs}$ 联系起来，由于其规律性和紧致性，RAR被认为体现了一种新的自然规律，与修正牛顿动力学（MOND）一致。以往对此关系的拟合受到先验期望的限制，局限于特定的函数形式，而ESR则允许在函数参数空间中进行几乎无先验的穷举搜索，以识别在准确性与简洁性之间最优权衡的方程。利用SPARC数据，我们发现最佳函数通常在高 $g_\text{bar}$ 下满足 $g_\text{obs} \propto g_\text{bar}$，虽然比例系数并不明确等于1，且当 $g_\text{bar} \to 0$ 时深层MOND极限 $g_\text{obs} \propto \sqrt{g_\text{bar}}$ 几乎不明显。通过根据有无外部场效应的MOND生成模拟数据，我们发现符号回归无法预期识别出生成函数或成功重建渐近斜率。我们得出结论，SPARC RAR的有限动力学范围及显著不确定性阻碍了对其函数形式的明确判定，因此仅凭这些数据既不能证明也不能排除类律引力行为。