Numerous phenomenological nuclear models have been proposed to describe specific observables within different regions of the nuclear chart. However, developing a unified model that describes the complex behavior of all nuclei remains an open challenge. Here, we explore whether novel symbolic Machine Learning (ML) can rediscover traditional nuclear physics models or identify alternatives with improved simplicity, fidelity, and predictive power. To address this challenge, we developed a Multi-objective Iterated Symbolic Regression approach that handles symbolic regressions over multiple target observables, accounts for experimental uncertainties and is robust against high-dimensional problems. As a proof of principle, we applied this method to describe the nuclear binding energies and charge radii of light and medium mass nuclei. Our approach identified simple analytical relationships based on the number of protons and neutrons, providing interpretable models with precision comparable to state-of-the-art nuclear models. Additionally, we integrated this ML-discovered model with an existing complementary model to estimate the limits of nuclear stability. These results highlight the potential of symbolic ML to develop accurate nuclear models and guide our description of complex many-body problems.

翻译：众多唯象核模型被提出，用以描述核素图中不同区域内的特定可观测量。然而，开发一个能够描述所有原子核复杂行为的统一模型仍然是一个开放的挑战。本文探讨了新颖的符号机器学习（ML）方法是否能够重新发现传统的核物理模型，或者识别出具有更高简洁性、保真度和预测能力的替代模型。为应对这一挑战，我们开发了一种多目标迭代符号回归方法，该方法能够处理针对多个目标观测量的符号回归，考虑实验不确定性，并对高维问题具有鲁棒性。作为原理验证，我们将此方法应用于描述轻核与中质量原子核的结合能及电荷半径。我们的方法发现了基于质子数与中子数的简单解析关系，提供了与最先进核模型精度相当的可解释模型。此外，我们将此机器学习发现的模型与一个现有的互补模型相结合，以估计核稳定性的极限。这些结果凸显了符号机器学习在开发精确核模型以及指导我们描述复杂多体问题方面的潜力。