Optimization of generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double-beta decay: ridge regression for nuclei with axial deformation

Abstract

The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. The computational complexity of the GCM increases rapidly with the number of collective coordinates. It imposes a strong restriction on the applicability of the method. In this work, we propose a subspace-reduction algorithm that employs optimal statistical ML models as surrogates for exact quantum-number projection calculations for norm and Hamiltonian kernels. The model space of the original GCM is reduced to a subspace relevant for nuclear low energy spectra and the NME of ground state to ground state $0\nu \beta \beta$ decay based on the orthogonality condition (OC) and the energy-transition-orthogonality procedure (ENTROP), respectively. For simplicity, the polynomial ridge regression (RR) algorithm is used to learn the norm and Hamiltonian kernels of axially deformed configurations. The efficiency and accuracy of this algorithm are illustrated for 76Ge and 76Se by comparing results obtained using the optimal RR models to direct GCM calculations. The low-lying energy spectra of ${}^{76}$Ge and ${}^{76}$Se, as well as the $0\nu \beta \beta$-decay NME between their ground states, are computed. The results show that the performance of the GCM+OC/ENTROP+RR is more robust than that of the GCM+RR alone, and the former can reproduce the results of the original GCM calculation accurately with a significantly reduced computational cost.

arXiv comment15 pages with 19 figures

References in corpus (69)

• A high-bias, low-variance introduction to Machine Learning for physicists
• New parametrization for the nuclear covariant energy density functional with point-coupling interaction
• Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
• Improved nuclear matter calculations from chiral low-momentum interactions
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
• Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay
• Energy density functional study of nuclear matrix elements for neutrinoless $\beta \beta$ decay
• Machine Learning in Nuclear Physics
• Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects
• Nuclear Mass Predictions for the Crustal Composition of Neutron Stars: A Bayesian Neural Network Approach
• Ab initio limits of atomic nuclei
• Mean field and beyond description of nuclear structure with the Gogny force: A review
• Bayesian approach to model-based extrapolation of nuclear observables
• Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of ${}^{48}$Ca
• Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics
• Shape and pairing fluctuations effects on neutrinoless double beta decay nuclear matrix elements
• Systematic study of nuclear matrix elements in neutrinoless double-beta decay with a beyond mean-field covariant density functional theory
• Low-momentum interaction in few-nucleon systems
• Predictions of nuclear $\beta$-decay half-lives with machine learning and their impacts on $r$ process
• Nuclear charge radii: Density functional theory meets Bayesian neural networks
• Eigenvector continuation with subspace learning
• Symmetry restoration in mean-field approaches
• Beyond Mean-Field Calculations for Odd-A Nuclei
• Global sensitivity analysis of bulk properties of an atomic nucleus
• Bayesian Evaluation of Incomplete Fission Yields
• Eigenvector Continuation as an Efficient and Accurate Emulator for Uncertainty Quantification
• Three-dimensional angular momentum projection in relativistic mean-field theory
• Nuclear mass predictions with machine learning reaching the accuracy required by $r$-process studies
• A microscopic benchmark-study of triaxiality in low-lying states of 76Kr
• Taming nuclear complexity with a committee of multilayer neural networks
• Nuclear matrix element of neutrinoless double-$\beta$ decay: Relativity and short-range correlations
• Study of Charge Radii with Neural Networks
• Relativistic description of nuclear matrix elements in neutrinoless double-$\beta$ decay
• Novel Bayesian neural network based approach for nuclear charge radii
• In-Medium Similarity Renormalization Group for Closed and Open-Shell Nuclei
• State-of-the-art of beyond mean field theories with nuclear density functionals
• Structure of Krypton isotopes calculated with symmetry conserving configuration mixing methods
• Generator-coordinate reference states for spectra and $0\nu \beta \beta$ decay in the in-medium similarity renormalization group
• Decoding Beta-Decay Systematics: A Global Statistical Model for Beta^- Halflives
• Multi-reference many-body perturbation theory for nuclei III -- Ab initio calculations at second order in PGCM-PT
• Efficient emulators for scattering using eigenvector continuation
• Multi-task learning on nuclear masses and separation energies with the kernel ridge regression
• Collective and Single-particle Motion in Beyond Mean Field Approaches
• Systematics of quadrupolar correlation energies
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• Nuclear energy density functionals from machine learning
• Anatomy of molecular structures in ${}^{20}$Ne
• Neutrinoless double-beta decay matrix elements in large shell-model spaces with the generator-coordinate method
• Toward emulating nuclear reactions using eigenvector continuation
• Global study of the spectroscopic properties of the first 2+ state in even-even nuclei
• Toward global beyond-mean-field calculations of nuclear masses and low-energy spectra
• Convergence of Eigenvector Continuation
• Ab initio benchmarks of neutrinoless double beta decay in light nuclei with a chiral Hamiltonian
• Generalizing the calculable $R$-matrix theory and eigenvector continuation to the incoming wave boundary condition
• Octupole correlations in low-lying states of 150Nd and 150Sm and their impact on neutrinoless double-beta decay
• Ground-state properties of even and odd Magnesium isotopes in a symmetry-conserving approach
• Configuration mixing calculation for complete low-lying spectra with the mean-field Hamiltonian
• Ab initio studies of double Gamow-Teller transition and its correlation with neutrinoless double beta decay
• Variation after parity projection calculation with Skyrme interaction for light nuclei
• The generator coordinate method in time-dependent density-functional theory: memory made simple
• The union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double-beta decay
• Variational calculation of many-body wave functions and energies from density-functional theory
• Application of efficient generator-coordinate subspace-selection algorithm to neutrinoless double-$\beta$ decay
• Generator Coordinate Truncations
• Variation after projection calculations for high-spin states
• Optimization of basis functions for the multi-configuration mixing using the Replica Exchange Monte-Carlo method and its application to ${}^{12}$C
• On interacting fermions and bosons with definite total momentum
• Optimization of the number of intrinsic states included in the discrete Generator Coordinate Method

Cited by in corpus (4)

• Ab initio uncertainty quantification of neutrinoless double-beta decay in ${}^{76}$Ge
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• Generator coordinate method for nuclear octupole excitations: status and perspectives
• Emulating generator coordinate method with extended eigenvector continuation: Lipkin-Meshkov-Glick model