Nuclear Dft Variational Eval

---
name: nuclear-dft-variational-eval
description: Evaluates a neural-network-based variational method for nuclear density functional theory by reproducing ground-state properties of finite nuclei and pasta phases, and benchmarking computational efficiency on GPU architectures. Use when the user wants to benchmark on Nuclear DFT Test Cases (Woods-Saxon, Finite Nuclei, Pasta Phases), or asks about evaluating this task. Reports binding energy.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2604.25759
  bibtex_key: yoshimura2026neuralvariational
  confidence: high
---

# nuclear-dft-variational-eval

> Neural-Network-Based Variational Method in Nuclear Density Functional Theory: Application to the Extended Thomas-Fermi Model — Yoshimura (2026) (arXiv:2604.25759, 2026)

## What this evaluates

Evaluates a neural-network-based variational method for nuclear density functional theory by reproducing ground-state properties of finite nuclei and pasta phases, and benchmarking computational efficiency on GPU architectures.

## Datasets

- **Nuclear DFT Test Cases (Woods-Saxon, Finite Nuclei, Pasta Phases)** — total ?; splits: test (-1)

## Metrics

- `binding energy` **(primary)** — range: percent
  - Relative deviation of calculated binding energy from reference ETF values: |BE_calc - BE_ref| / |BE_ref|.
- `total energy deviation` — range: percent
  - Relative difference between calculated total energy and reference value (-1323.2 MeV) for the Woods-Saxon benchmark.
- `computational time per 1000 steps` — range: other
  - Wall-clock time required to complete 1000 optimization steps, measured on NVIDIA H100 and RTX 5000 Ada GPUs under single and double precision.

## Input / output format

**Input**: Nuclear density parameterized by a multilayer perceptron (MLP) with N_perc perceptrons, optimized by minimizing a Skyrme-type energy functional. For pasta phases, a guide potential V_guide(r) is added.

**Output**: Ground-state nuclear density distribution, total binding energy, neutron/proton radii, and optimization convergence time.

## Scoring recipe

```python
def compute_metrics(pred, gold):
    be_rel_err = abs(pred['BE'] - gold['BE']) / abs(gold['BE'])
    r_n_err = abs(pred['r_n'] - gold['r_n']) / gold['r_n']
    r_p_err = abs(pred['r_p'] - gold['r_p']) / gold['r_p']
    return {
        'binding energy': be_rel_err,
        'neutron radius error': r_n_err,
        'proton radius error': r_p_err
    }
```

## Common pitfalls

- Differences in discretization (1D spherical vs 3D non-symmetric) and mesh spacing (0.1 fm vs 0.5 fm) cause apparent discrepancies in radii that are not method failures.
- Single-precision arithmetic yields nearly identical physical results to double-precision, but computational time scaling differs significantly between GPU architectures.

## Evidence (verbatim from paper)

> These results show that the NN-based calculations are in good agreement with the previous ETF calculations. More specifically, the difference in the binding energy is at most about 0.5%, while the radii differ by approximately 1% or less.

## Citation

```bibtex
@misc{yoshimura2026neuralvariational,
  title={Neural-Network-Based Variational Method in Nuclear Density Functional Theory: Application to the Extended Thomas-Fermi Model},
  author={Yoshimura (2026)},
  year={2026},
  note={arXiv:2604.25759}
}
```

- arXiv: 2604.25759