发表机构
INSANE Group, IIT, NCSR Demokritos; Department of Physics, University of Thessaly（希腊国家科学研究中心德谟克利特研究所; 塞萨洛尼基大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出概率物理信息框架，结合WaveNet和ParamNet，从稀疏谱数据识别Woods-Saxon参数，验证了正演-反演耦合方法的有效性。
AI 中文摘要
Woods-Saxon平均场方法为有限核中束缚单粒子运动提供了紧凑的描述，而物理信息神经网络（PINNs）为从稀疏谱数据恢复势参数的反演问题提供了一条可微分的路径。我们开发了一个概率物理信息框架，其中WaveNet表示分离的单粒子波函数，ParamNet将选定的谱、核描述符和量子数映射到六个全局Woods-Saxon参数上的学习分布。哈密顿量包括中心Woods-Saxon项、质子库仑项和自旋-轨道项；训练强制谱能量一致性、薛定谔方程残差、边界条件、归一化、正交性、自旋-轨道劈裂约束和潜在正则化。分布均值作为无选择参数估计，通过与独立的有限差分径向求解器验证。使用Seminole和Wahlborn参数化的合成闭合测试恢复了所有六个参数，相对误差低于百分之一，并再现了参考谱，平均绝对偏差分别为0.0109和0.0131 MeV。对于使用Wahlborn形式的实验谱，估计器将所有态平均绝对误差从1.0783降至0.8303 MeV；使用Seminole形式时达到0.8068 MeV，接近Seminole参考参数的0.7969 MeV，仅使用42个实验能级——比Seminole校准少约51%。这些结果表明，稀疏、结构化的单粒子谱可以在可微分框架内约束全局Woods-Saxon相互作用，同时解决正演特征值问题和反演参数识别，而学习到的输出分布提供了模型派生的、定性的参数刚度度量。
英文摘要
The Woods-Saxon mean-field approach offers a compact description of bound single-particle motion in finite nuclei, while physics-informed neural networks (PINNs) provide a differentiable route to the inverse problem of recovering potential parameters from sparse spectral data. We develop a probabilistic physics-informed framework in which a WaveNet represents the separated single-particle wavefunction and a ParamNet maps selected spectra, nuclear descriptors, and quantum numbers to a learned distribution over six global Woods-Saxon parameters. The Hamiltonian includes the central Woods-Saxon, proton Coulomb, and spin-orbit terms; training enforces spectral energy consistency, Schr"odinger-equation residuals, boundary conditions, normalization, orthogonality, spin-orbit splitting constraints, and latent regularization. The distribution mean serves as a selection-free parameter estimate, validated against an independent finite-difference radial solver. Synthetic closure tests with the Seminole and Wahlborn parameterizations recover all six parameters with sub-percent relative errors and reproduce reference spectra with mean absolute deviations of (0.0109) and (0.0131~\mathrm{MeV}). For experimental spectra with the Wahlborn form, the estimator reduces the all-state mean absolute error from (1.0783) to (0.8303~\mathrm{MeV}); with the Seminole form it attains (0.8068~\mathrm{MeV}), close to the (0.7969~\mathrm{MeV}) from Seminole reference parameters, using only (42) experimental levels -- about (51%) fewer than the Seminole calibration. These results show that sparse, structured single-particle spectra can constrain global Woods-Saxon interactions within a differentiable framework addressing both the forward eigenvalue problem and inverse parameter identification, while the learned output spread offers a model-derived, qualitative measure of parameter stiffness.
Comments29 pages, 4 figures, 12 tables
