Neural-Network-Based Variational Method in Nuclear Density Functional Theory: Application to the Extended Thomas-Fermi Model
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918492181102592 |
|---|---|
| author | Yoshimura, Kenta |
| author_facet | Yoshimura, Kenta |
| contents | We propose a neural-network-based variational framework for nuclear Density Functional Theory based on the extended Thomas--Fermi (ETF) model, in which proton and neutron number densities are represented by multilayer perceptrons and determined by direct minimization of a Skyrme-type energy density functional. We clarify the mathematical connection to the conventional Euler--Lagrange formulation, showing that stationarity in parameter space corresponds to a projected Euler--Lagrange condition on the neural-network trial-density manifold. The basic validity of the framework is examined through three sets of calculations: a Woods--Saxon potential benchmark, ground-state calculations of finite nuclei ($^{40}$Ca, $^{90}$Zr, and $^{208}$Pb), and nuclear pasta phases. The binding energies of finite nuclei agree with existing ETF calculations to within $0.5\%$, and representative pasta structures including spheres, rods, and slabs are reproduced. We also find that single-precision arithmetic yields results comparable to double precision, suggesting that the present framework is well suited to GPU environments in which low-precision computation is advantageous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25759 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Neural-Network-Based Variational Method in Nuclear Density Functional Theory: Application to the Extended Thomas-Fermi Model Yoshimura, Kenta Nuclear Theory We propose a neural-network-based variational framework for nuclear Density Functional Theory based on the extended Thomas--Fermi (ETF) model, in which proton and neutron number densities are represented by multilayer perceptrons and determined by direct minimization of a Skyrme-type energy density functional. We clarify the mathematical connection to the conventional Euler--Lagrange formulation, showing that stationarity in parameter space corresponds to a projected Euler--Lagrange condition on the neural-network trial-density manifold. The basic validity of the framework is examined through three sets of calculations: a Woods--Saxon potential benchmark, ground-state calculations of finite nuclei ($^{40}$Ca, $^{90}$Zr, and $^{208}$Pb), and nuclear pasta phases. The binding energies of finite nuclei agree with existing ETF calculations to within $0.5\%$, and representative pasta structures including spheres, rods, and slabs are reproduced. We also find that single-precision arithmetic yields results comparable to double precision, suggesting that the present framework is well suited to GPU environments in which low-precision computation is advantageous. |
| title | Neural-Network-Based Variational Method in Nuclear Density Functional Theory: Application to the Extended Thomas-Fermi Model |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2604.25759 |