# Discovering Nuclear Models from Symbolic Machine Learning

arXiv: https://arxiv.org/abs/2404.11477 · HTML: https://mlsanity.com/paper/2404.11477/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 74 references that are in the map.
- First posted on arXiv 17 Apr 2024.

## Builds on (most cited first, 14 of 14)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate](https://mlsanity.com/paper/1806.05161/) (2018)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge](https://mlsanity.com/paper/2209.06257/) (2022)
- [Fast, accurate, and transferable many-body interatomic potentials by symbolic regression](https://mlsanity.com/paper/1904.01095/) (2019)
- [Analytical Modelling of Exoplanet Transit Specroscopy with Dimensional Analysis and Symbolic Regression](https://mlsanity.com/paper/2112.11600/) (2021)
- [Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression](https://mlsanity.com/paper/2211.08420/) (2022)
- [Constructing Parsimonious Analytic Models for Dynamic Systems via Symbolic Regression](https://mlsanity.com/paper/1903.11483/) (2019)
- [SymbolNet: Neural Symbolic Regression with Adaptive Dynamic Pruning for Compression](https://mlsanity.com/paper/2401.09949/) (2024)
- [Bayesian approach to model-based extrapolation of nuclear observables](https://mlsanity.com/paper/1806.00552/) (2018)
- [NuCLR: Nuclear Co-Learned Representations](https://mlsanity.com/paper/2306.06099/) (2023)

## Built on by (most cited first, 1 of 1)

- [Product units in gated recurrent units improve nuclear-mass prediction](https://mlsanity.com/paper/2606.06866/) (2026)

## Abstract (arXiv)

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.