Discovering Nuclear Models from Symbolic Machine Learning
arXiv:2404.11477 · doi:10.1038/s42005-025-02023-2
Abstract
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.
References in corpus (35)
- XGBoost: A Scalable Tree Boosting System
- Modern Theory of Nuclear Forces
- Nuclear energy density optimization: Large deformations
- Unexpectedly large charge radii of neutron-rich calcium isotopes
- Symbolic Regression in Materials Science
- The CAMELS project: Cosmology and Astrophysics with MachinE Learning Simulations
- Quantifying truncation errors in effective field theory
- Discovering Symbolic Models from Deep Learning with Inductive Biases
- Global performance of covariant energy density functionals: ground state observables of even-even nuclei and the estimate of theoretical uncertainties
- Ab initio limits of atomic nuclei
- Unified ab initio approaches to nuclear structure and reactions
- Bayesian approach to model-based extrapolation of nuclear observables
- Laser Spectroscopy for the Study of Exotic Nuclei
- Charge radii of exotic potassium isotopes challenge nuclear theory and the magic character of
- Towards the global description of nuclear charge radii: exploring the Fayans energy density functional
- Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression
- Machine learning the nuclear mass
- A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge
- Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws
- Laser spectroscopy of neutron-rich Hg isotopes: Illuminating the kink and odd-even staggering in charge radii across the shell closure
- Nuclear Charge Radii of the Nickel Isotopes Ni
- Charge radii in covariant density functional theory: a global view
- The anatomy of the simplest Duflo-Zuker mass formula
- Extrapolation of nuclear structure observables with artificial neural networks
- Physically Interpretable Machine Learning for nuclear masses
- New Ideas in Constraining Nuclear Forces
- Changes in nuclear structure along the Mn isotopic chain studied via charge radii
- Progress and Challenges in Ab Initio Simulations of Quantum Nuclei in Weakly Bonded Systems
- Nuclear DFT analysis of electromagnetic moments in odd near doubly magic nuclei
- Electromagnetic Properties of Indium Isotopes Elucidate the Doubly Magic Character of Sn
- Constructing Parsimonious Analytic Models for Dynamic Systems via Symbolic Regression
- Predicting Beta Decay Energy with Machine Learning
- Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression
- SymbolNet: Neural Symbolic Regression with Adaptive Dynamic Pruning for Compression
- Artificial Intelligence Supported Shell-Model Calculations for Light Sn Isotopes